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A new type of high-order multi-resolution trigonometric WENO schemes with adaptive linear weights for hyperbolic conservation laws 一种新型高阶多分辨率三角函数 WENO 方案,具有双曲守恒定律的自适应线性权重
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-20 DOI: 10.1016/j.compfluid.2024.106372
Yan Zhang , Jun Zhu
{"title":"A new type of high-order multi-resolution trigonometric WENO schemes with adaptive linear weights for hyperbolic conservation laws","authors":"Yan Zhang ,&nbsp;Jun Zhu","doi":"10.1016/j.compfluid.2024.106372","DOIUrl":"10.1016/j.compfluid.2024.106372","url":null,"abstract":"<div><p>This article provides a series of high-order multi-resolution trigonometric weighted essentially non-oscillatory schemes with adaptive linear weights for solving hyperbolic conservation laws in a finite difference framework, which are termed as the MR-TWENO-ALW schemes. These new TWENO schemes only use the information defined on two unequal-sized spatial stencils and do not need to introduce other stencils to achieve optimal high-order accuracy. To increase the flexibility of the linear weights, we design an adaptive linear weight process which is an automatic adjustment of two linear weights with two simple conditions. This ensures the schemes to get the optimal order of accuracy in smooth regions, accurately approximate sharp gradients, and suppress high oscillations near strong discontinuities. These new MR-TWENO-ALW schemes can achieve high spectral resolution and maintain low computational cost in large scale engineering applications. And these new schemes are simple in the construction and could be extended to arbitrarily high-order accuracy on other computing meshes. Extensive one-dimensional and two-dimensional numerical examples are used to testify the feasibility of these new MR-TWENO-ALW schemes.</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"281 ","pages":"Article 106372"},"PeriodicalIF":2.5,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141841154","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}
引用次数: 0
Inconsistencies in unstructured geometric volume-of-fluid methods for two-phase flows with high density ratios 针对高密度比两相流的非结构化几何流体力学方法的不一致性
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-20 DOI: 10.1016/j.compfluid.2024.106375
Jun Liu , Tobias Tolle , Davide Zuzio , Jean-Luc Estivalèzes , Santiago Marquez Damian , Tomislav Marić
{"title":"Inconsistencies in unstructured geometric volume-of-fluid methods for two-phase flows with high density ratios","authors":"Jun Liu ,&nbsp;Tobias Tolle ,&nbsp;Davide Zuzio ,&nbsp;Jean-Luc Estivalèzes ,&nbsp;Santiago Marquez Damian ,&nbsp;Tomislav Marić","doi":"10.1016/j.compfluid.2024.106375","DOIUrl":"10.1016/j.compfluid.2024.106375","url":null,"abstract":"<div><p>Geometric flux-based Volume-of-Fluid (VOF) methods (Marić et al., 2020) are widely considered consistent in handling two-phase flows with high density ratios. However, although the conservation of mass and momentum is consistent for two-phase incompressible single-field Navier–Stokes equations without phase-change (Liu et al., 2023), discretization may easily introduce inconsistencies that result in very large errors or catastrophic failure. We apply the consistency conditions derived for the <span><math><mi>ρ</mi></math></span>LENT unstructured Level Set/Front Tracking method (Liu et al., 2023) to flux-based geometric VOF methods (Marić et al., 2020), and implement our discretization into the plicRDF-isoAdvector geometrical VOF method (Roenby et al., 2016). We find that computing the mass flux by scaling the geometrically computed fluxed phase-specific volume can ensure equivalence between the mass conservation equation and the phase indicator (volume conservation) if consistent discretization schemes are chosen for the temporal and convective term. Based on the analysis of discretization errors, we suggest a consistent combination of the temporal discretization scheme and the interpolation scheme for the momentum convection term. We confirm the consistency by solving an auxiliary mass conservation equation with a geometrical calculation of the face-centered density (Liu et al., 2023). We prove the equivalence between these two approaches mathematically and verify and validate their numerical stability for density ratios within [1, <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>6</mn></mrow></msup></mrow></math></span>] and viscosity ratios within [<span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>, <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>5</mn></mrow></msup></mrow></math></span>].</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"281 ","pages":"Article 106375"},"PeriodicalIF":2.5,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S004579302400207X/pdfft?md5=d79e98a6cf675e23503f97b1bf9e1d18&pid=1-s2.0-S004579302400207X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141960722","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}
引用次数: 0
REV-Scale study of miscible density-driven convection in porous media REV--多孔介质中混杂密度驱动对流的尺度研究
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-20 DOI: 10.1016/j.compfluid.2024.106376
You Meng , Yifan Wang , Zhenghao Sun , Haoyu Wang , Yujun Chen , Gaojie Liu
{"title":"REV-Scale study of miscible density-driven convection in porous media","authors":"You Meng ,&nbsp;Yifan Wang ,&nbsp;Zhenghao Sun ,&nbsp;Haoyu Wang ,&nbsp;Yujun Chen ,&nbsp;Gaojie Liu","doi":"10.1016/j.compfluid.2024.106376","DOIUrl":"10.1016/j.compfluid.2024.106376","url":null,"abstract":"<div><p>Miscible density-driven convection in porous media has important implications for the long-term security of geological <span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span> sequestration. In this study, a REV-scale lattice Boltzmann equation method based on the generalized Navier–Stokes equations was used to simulate density-driven convection in porous media, Thus, the effects of the Rayleigh number, the Darcy number, the Schmidt number, and the porosity of porous media can be discussed separately. The results show that density-driven convection only occurs when the Rayleigh–Darcy–Schmidt number <span><math><msub><mrow><mtext>Ra</mtext></mrow><mrow><mtext>D-S</mtext></mrow></msub></math></span> exceeds <span><math><mrow><mn>1</mn><msup><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msup></mrow></math></span>. The larger the Ra, the more disordered the concentration field, the earlier the convective phenomenon begins, and the more significant the convective mixing; The larger the Da, the finer the generated fingers. These findings provide important insights for the development of geological sequestration technologies.</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"281 ","pages":"Article 106376"},"PeriodicalIF":2.5,"publicationDate":"2024-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141839389","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}
引用次数: 0
Quantitative comparison of variational and sequential data assimilation techniques for one-dimensional initial-value problems of ideal MHD 理想 MHD 一维初值问题的变分和顺序数据同化技术的定量比较
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-18 DOI: 10.1016/j.compfluid.2024.106373
J.H. Arnal, C.P.T. Groth
{"title":"Quantitative comparison of variational and sequential data assimilation techniques for one-dimensional initial-value problems of ideal MHD","authors":"J.H. Arnal,&nbsp;C.P.T. Groth","doi":"10.1016/j.compfluid.2024.106373","DOIUrl":"10.1016/j.compfluid.2024.106373","url":null,"abstract":"<div><p>State-of-the-art predictions of the solar-wind and space weather phenomena are today largely based on the equations of magnetohydrodynamics (MHD). Despite their sophistication and success, the forecasting potential of global MHD models is often undermined by uncertainties in model inputs; the initial and boundary conditions are generally not known and must be estimated. This study therefore investigates the use of data assimilation strategies to minimize forecast errors in the context of initial-value problems of the one-dimensional ideal MHD equations. Several canonical MHD wave propagation problems involving both smooth and discontinuous solutions, including those having strongly non-linear behaviour with shocks, are considered in a set of twin experiments with varying synthetic observational data sparsity. Two data assimilation strategies are quantitatively compared, namely the Ensemble Kalman Filter (EnKF) and strong-constraint variational data assimilation. For the latter, the necessary adjoint model is derived, summarized, and validated. The study represents the first use of variational data assimilation applied to ideal magnetohydrodynamics and demonstrates its potential advantages over sequential approaches. In particular, for the numerical experiments considered herein, it is found that the variational approach consistently achieved superior performance and stability compared to the EnKF method. In addition, two different strategies for mitigating data assimilation induced errors associated with violation of the divergence-free property of the magnetic field are introduced and assessed. Finally, the present study provides the technical background and quantitative justification for future investigations of variational data assimilation aimed at enhancing three-dimensional simulations of the solar wind and space weather processes.</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"282 ","pages":"Article 106373"},"PeriodicalIF":2.5,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141850613","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}
引用次数: 0
Two quantum algorithms for solving the one-dimensional advection–diffusion equation 求解一维平流扩散方程的两种量子算法
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-18 DOI: 10.1016/j.compfluid.2024.106369
Julia Ingelmann , Sachin S. Bharadwaj , Philipp Pfeffer , Katepalli R. Sreenivasan , Jörg Schumacher
{"title":"Two quantum algorithms for solving the one-dimensional advection–diffusion equation","authors":"Julia Ingelmann ,&nbsp;Sachin S. Bharadwaj ,&nbsp;Philipp Pfeffer ,&nbsp;Katepalli R. Sreenivasan ,&nbsp;Jörg Schumacher","doi":"10.1016/j.compfluid.2024.106369","DOIUrl":"10.1016/j.compfluid.2024.106369","url":null,"abstract":"<div><p>Two quantum algorithms are presented for the numerical solution of a linear one-dimensional advection–diffusion equation with periodic boundary conditions. Their accuracy and performance with increasing qubit number are compared point-by-point with each other. Specifically, we solve the linear partial differential equation with a Quantum Linear Systems Algorithm (QLSA) based on the Harrow–Hassidim–Lloyd method and a Variational Quantum Algorithm (VQA), for resolutions that can be encoded using up to 6 qubits, which corresponds to <span><math><mrow><mi>N</mi><mo>=</mo><mn>64</mn></mrow></math></span> grid points on the unit interval. Both algorithms are hybrid in nature, i.e., they involve a combination of classical and quantum computing building blocks. The QLSA and VQA are solved as ideal statevector simulations using the in-house solver QFlowS and open-access Qiskit software, respectively. We discuss several aspects of both algorithms which are crucial for a successful performance in both cases. These are the accurate eigenvalue estimation with the quantum phase estimation for the QLSA and the choice of the algorithm of the minimization of the cost function for the VQA. The latter algorithm is also implemented in the noisy Qiskit framework including measurement noise. We reflect on the current limitations and suggest some possible routes of future research for the numerical simulation of classical fluid flows on a quantum computer.</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"281 ","pages":"Article 106369"},"PeriodicalIF":2.5,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045793024002019/pdfft?md5=33d0c599592af889ca32afc28167dd15&pid=1-s2.0-S0045793024002019-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141954294","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}
引用次数: 0
Efficient parallel solver for rarefied gas flow using GSIS 利用 GSIS 实现稀薄气体流动的高效并行求解器
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-18 DOI: 10.1016/j.compfluid.2024.106374
Yanbing Zhang, Jianan Zeng, Ruifeng Yuan, Wei Liu, Qi Li, Lei Wu
{"title":"Efficient parallel solver for rarefied gas flow using GSIS","authors":"Yanbing Zhang,&nbsp;Jianan Zeng,&nbsp;Ruifeng Yuan,&nbsp;Wei Liu,&nbsp;Qi Li,&nbsp;Lei Wu","doi":"10.1016/j.compfluid.2024.106374","DOIUrl":"10.1016/j.compfluid.2024.106374","url":null,"abstract":"<div><p>Recently, the general synthetic iterative scheme (GSIS) has been proposed to find the steady-state solution of the Boltzmann equation in the whole range of gas rarefaction, where its fast-converging and asymptotic-preserving properties lead to the significant reduction of iteration numbers and spatial cells in the near-continuum flow regime. However, the efficiency and accuracy of GSIS have only been demonstrated in two-dimensional problems with small numbers of spatial cells and discrete velocities. Here, a large-scale parallel computing strategy is designed to extend the GSIS to three-dimensional flow problems, including the supersonic flows which are usually difficult to solve by the discrete velocity method. Since the GSIS involves the calculation of the mesoscopic kinetic equation which is defined in six-dimensional phase-space, and the macroscopic high-temperature Navier–Stokes–Fourier equations in three-dimensional physical space, the proper partition of the spatial and velocity spaces, and the allocation of CPU cores to the mesoscopic and macroscopic solvers, are the keys to improving the overall computational efficiency. These factors are systematically tested to achieve optimal performance, up to 100 billion spatial and velocity grids. For hypersonic flows around the Apollo reentry capsule, the X38-like vehicle, and the space station, our parallel solver can obtain the converged solution within one hour.</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"281 ","pages":"Article 106374"},"PeriodicalIF":2.5,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141943847","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}
引用次数: 0
GPU optimized multi-block-multi-mesh immersed boundary method for flows in complex arterial models 针对复杂动脉模型流动的 GPU 优化多区块多网格沉浸边界法
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-15 DOI: 10.1016/j.compfluid.2024.106367
Debajyoti Kumar , Siddharth D. Sharma , Somnath Roy
{"title":"GPU optimized multi-block-multi-mesh immersed boundary method for flows in complex arterial models","authors":"Debajyoti Kumar ,&nbsp;Siddharth D. Sharma ,&nbsp;Somnath Roy","doi":"10.1016/j.compfluid.2024.106367","DOIUrl":"10.1016/j.compfluid.2024.106367","url":null,"abstract":"<div><p>Immersed boundary method (IBM) is widely used for simulating flow in complex geometries using structured grids. However, this entails a disadvantage when simulating internal flows through curved and bent tubes. The presence of grids outside the fluid domain leads to the wastage of memory and computational overheads. Here, we propose a multi-block-multi-mesh framework to capture the complex geometry using multiple grid blocks fitted close to the body, reducing excess grids. This also has the advantage of using different and non-uniform grid spacing in different blocks. The reduction of the grid enables encompassing bigger caseloads on a single GPU. The solver is accelerated on GPU using OpenACC, compared to sequential CPU simulations, and speedup is presented. The speedup obtained is comparable to that of large multicore systems. The framework is extensively validated for straight artery with axisymmetric stenosis and bileaflet mechanical heart valve with axisymmetric sinus. This framework then models complex arterial flows like stenosed aorta, patient-specific branched aorta, bileaflet mechanical heart valve with Valsalva sinus and aorta, and lastly, patient-specific iliac aortic aneurysm. This framework achieves a significant reduction in GPU memory requirement for complex arterial models, enabling us to perform direct numerical simulation (DNS) of the stenosed aorta and mechanical heart valve cases in a single GPU.</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"281 ","pages":"Article 106367"},"PeriodicalIF":2.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141716454","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}
引用次数: 0
Third-order numerical scheme for Euler equations of gas dynamics using Jordan canonical based splitting flux 使用基于约旦典范的分裂通量的气体动力学欧拉方程三阶数值方案
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-15 DOI: 10.1016/j.compfluid.2024.106370
Bao-Shan Wang , Naveen Kumar Garg
{"title":"Third-order numerical scheme for Euler equations of gas dynamics using Jordan canonical based splitting flux","authors":"Bao-Shan Wang ,&nbsp;Naveen Kumar Garg","doi":"10.1016/j.compfluid.2024.106370","DOIUrl":"10.1016/j.compfluid.2024.106370","url":null,"abstract":"<div><p>We propose third-order A-WENO finite difference schemes that are based on the recently introduced first-order numerical schemes in [N. K. Garg et al., Journal of Computational Physics, 407(2020)] for the systems of compressible Euler equations of gas dynamics. The convective components of these schemes (fluxes), both in one- and multi-dimensions, are free from complicated Riemann solvers. Third-order characteristic-wise WENO-Z interpolations are employed to obtain the third-order point values required for the numerical fluxes. To demonstrate the robustness and accuracy of the resulting schemes, we compare the numerical results with local Lax–Friedrichs (LLF) and Harten–Lax–van Leer (HLL) fluxes on various one- and two-dimensional examples. The obtained results outperform LLF and HLL fluxes in terms of enhancing the resolution of contact waves, especially near isolated steady and moving contact discontinuities, as well as in accurately resolving high-frequency waves in one dimension (1-D) and the small-scale structures in two dimensions (2-D).</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"281 ","pages":"Article 106370"},"PeriodicalIF":2.5,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141712072","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}
引用次数: 0
An artificial compressibility approach to solve low Mach number flows in closed domains 解决封闭域中低马赫数流动的人工可压缩性方法
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-11 DOI: 10.1016/j.compfluid.2024.106364
A. Beccantini , C. Corre , S. Gounand , C.-H. Phan
{"title":"An artificial compressibility approach to solve low Mach number flows in closed domains","authors":"A. Beccantini ,&nbsp;C. Corre ,&nbsp;S. Gounand ,&nbsp;C.-H. Phan","doi":"10.1016/j.compfluid.2024.106364","DOIUrl":"10.1016/j.compfluid.2024.106364","url":null,"abstract":"<div><p>An artificial compressibility approach is proposed to compute the solution of the compressible equations in the low Mach number limit, in closed domain with moving boundaries. The low Mach number stiffness is reduced by introducing an artificial sound speed, much lower than the physical one. This allows to avoid both the acoustic time step restriction and the loss of accuracy of classical compressible solvers, without solving a Poisson equation for the pressure or using the time-implicit discretization of the Turkel-type preconditioning technique. Moreover the proposed formulation involves the conservative variables plus the dynamic pressure, which facilitates the implementation of the approach in classical CFD codes for compressible flows. The numerical experiments presented show that the approach is both accurate and CPU efficient.</p></div>","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"280 ","pages":"Article 106364"},"PeriodicalIF":2.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0045793024001968/pdfft?md5=3c1e8f8f18e0eb1776c399c9dc23ba2d&pid=1-s2.0-S0045793024001968-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141629805","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}
引用次数: 0
Mechanism of collision and drainage of liquid droplet around sphere placed within a hollow cylinder 置于空心圆筒内的球体周围液滴的碰撞和排泄机理
IF 2.5 3区 工程技术
Computers & Fluids Pub Date : 2024-07-11 DOI: 10.1016/j.compfluid.2024.106365
Prakasha Chandra Sahoo , Jnana Ranjan Senapati , Basanta Kumar Rana
{"title":"Mechanism of collision and drainage of liquid droplet around sphere placed within a hollow cylinder","authors":"Prakasha Chandra Sahoo ,&nbsp;Jnana Ranjan Senapati ,&nbsp;Basanta Kumar Rana","doi":"10.1016/j.compfluid.2024.106365","DOIUrl":"10.1016/j.compfluid.2024.106365","url":null,"abstract":"&lt;div&gt;&lt;p&gt;It is attempted earnestly to elucidate the mechanism of collision and drainage of liquid mass around the spherical substrate suspended within the hollow cylinder using Gerris open-source code by employing Volume of Fluid (VOF) methodology. Various influencing parameters, namely, sphere-to-droplet diameter ratio &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, Weber number&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mspace&gt;&lt;/mspace&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, Ohnesorge number &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, and Bond number&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; are employed to observe the drainage mechanism through the constricted path. The pattern of the interfacial morphology of droplet collision and drainage mechanism is presented using numerical contours. It is important to mention herein that the droplet undergoes several important stages like collision, cap formation, engulfment, drainage, and pinch-off. The passage between the sphere and the cylinder is sufficiently wider at a lower value of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; due to which the liquid mass is drained out completely without any hindrance. The drainage process becomes considerably faster at a higher &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; compared to a lower &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. In addition, the flow of liquid mass through the passage gets delayed at a greater &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; than a lower &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;O&lt;/mi&gt;&lt;mi&gt;h&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; assuming a given value of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. The liquid drop requires less time to pass through the constricted path at lower &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; for a given value of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;W&lt;/mi&gt;&lt;mi&gt;e&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. We have also attempted to quantify the drainage of liquid volume passes through the passage, which is denoted as &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mrow&gt;&lt;msup&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;/mrow&gt;&lt;mo&gt;*&lt;/mo&gt;&lt;/msup&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. One can notice the increasing pattern of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;Q&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/msub&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; with continuous progress of time stamp for all cases of &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;s&lt;/mi&gt;&lt;/msub&gt;&lt;mo&gt;/&lt;/mo&gt;&lt;msub&gt;&lt;mi&gt;D&lt;/mi&gt;&lt;mi&gt;o&lt;/mi&gt;&lt;/msub","PeriodicalId":287,"journal":{"name":"Computers & Fluids","volume":"281 ","pages":"Article 106365"},"PeriodicalIF":2.5,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141701950","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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