Süleyman Cengizci , Hakan F. Öztop , Gülden Mülayim
{"title":"在不同温度边界条件下,对充满纳米流体的方形空腔中的自然对流进行稳定有限元模拟","authors":"Süleyman Cengizci , Hakan F. Öztop , Gülden Mülayim","doi":"10.1016/j.icheatmasstransfer.2024.107655","DOIUrl":null,"url":null,"abstract":"<div><p>Natural convection heat transfer phenomena in nanofluid-filled square cavities with various temperature boundary conditions are studied computationally. From electronic cooling to building ventilation systems, such phenomena have numerous practical applications, and accurate simulations are crucial for developing new designs. Towards that end, the Navier–Stokes equations of incompressible flows are considered with thermal coupling. The base fluid is pure water, the nanoparticles are copper (Cu), cupric oxide (CuO), or aluminum oxide (Al<sub>2</sub>O<sub>3</sub>), and the nanofluids are assumed to be homogeneous. It is well known that, in the standard finite element method framework, inappropriate selection of interpolation functions, e.g., (bi-)linear equal-order-interpolation velocity-pressure (e.g., <span><math><msub><mi>P</mi><mn>1</mn></msub><msub><mi>P</mi><mn>1</mn></msub></math></span> and <span><math><msub><mi>Q</mi><mn>1</mn></msub><msub><mi>Q</mi><mn>1</mn></msub></math></span>) elements, yields nonphysical oscillations in the flow field for simulating incompressible flows, particularly for high Rayleigh numbers. In this study, in order to overcome such numerical instability issues, the streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) finite element formulations are utilized. The SUPG/PSPG-stabilized (SUPS) formulation is also enhanced with the least-squares on incompressibility constraint (LSIC). A comprehensive set of numerical test computations is considered for the values of the Rayleigh numbers ranging from <span><math><msup><mn>10</mn><mn>3</mn></msup></math></span> to <span><math><msup><mn>10</mn><mn>6</mn></msup></math></span> and a broad range of volume fractions of nanoparticles from <span><math><mi>ϕ</mi><mo>=</mo><mn>0.025</mn></math></span> to <span><math><mi>ϕ</mi><mo>=</mo><mn>0.2</mn></math></span>. Incompressible flow solvers are developed in-house and executed in parallel. Numerical simulations and comparisons with reported studies reveal that the proposed formulation performs quite well even at high Rayleigh numbers, and it does not exhibit any significant local or globally spread numerical instabilities. It is also noted that this is achieved without employing any adaptive mesh strategies and using only linear and equal-order interpolation functions, which in turn saves computational time.</p></div>","PeriodicalId":332,"journal":{"name":"International Communications in Heat and Mass Transfer","volume":null,"pages":null},"PeriodicalIF":6.4000,"publicationDate":"2024-06-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stabilized finite element simulation of natural convection in square cavities filled with nanofluids under various temperature boundary conditions\",\"authors\":\"Süleyman Cengizci , Hakan F. Öztop , Gülden Mülayim\",\"doi\":\"10.1016/j.icheatmasstransfer.2024.107655\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Natural convection heat transfer phenomena in nanofluid-filled square cavities with various temperature boundary conditions are studied computationally. From electronic cooling to building ventilation systems, such phenomena have numerous practical applications, and accurate simulations are crucial for developing new designs. Towards that end, the Navier–Stokes equations of incompressible flows are considered with thermal coupling. The base fluid is pure water, the nanoparticles are copper (Cu), cupric oxide (CuO), or aluminum oxide (Al<sub>2</sub>O<sub>3</sub>), and the nanofluids are assumed to be homogeneous. It is well known that, in the standard finite element method framework, inappropriate selection of interpolation functions, e.g., (bi-)linear equal-order-interpolation velocity-pressure (e.g., <span><math><msub><mi>P</mi><mn>1</mn></msub><msub><mi>P</mi><mn>1</mn></msub></math></span> and <span><math><msub><mi>Q</mi><mn>1</mn></msub><msub><mi>Q</mi><mn>1</mn></msub></math></span>) elements, yields nonphysical oscillations in the flow field for simulating incompressible flows, particularly for high Rayleigh numbers. In this study, in order to overcome such numerical instability issues, the streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) finite element formulations are utilized. The SUPG/PSPG-stabilized (SUPS) formulation is also enhanced with the least-squares on incompressibility constraint (LSIC). A comprehensive set of numerical test computations is considered for the values of the Rayleigh numbers ranging from <span><math><msup><mn>10</mn><mn>3</mn></msup></math></span> to <span><math><msup><mn>10</mn><mn>6</mn></msup></math></span> and a broad range of volume fractions of nanoparticles from <span><math><mi>ϕ</mi><mo>=</mo><mn>0.025</mn></math></span> to <span><math><mi>ϕ</mi><mo>=</mo><mn>0.2</mn></math></span>. Incompressible flow solvers are developed in-house and executed in parallel. Numerical simulations and comparisons with reported studies reveal that the proposed formulation performs quite well even at high Rayleigh numbers, and it does not exhibit any significant local or globally spread numerical instabilities. It is also noted that this is achieved without employing any adaptive mesh strategies and using only linear and equal-order interpolation functions, which in turn saves computational time.</p></div>\",\"PeriodicalId\":332,\"journal\":{\"name\":\"International Communications in Heat and Mass Transfer\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":6.4000,\"publicationDate\":\"2024-06-07\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Communications in Heat and Mass Transfer\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0735193324004172\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MECHANICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Communications in Heat and Mass Transfer","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0735193324004172","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MECHANICS","Score":null,"Total":0}
Stabilized finite element simulation of natural convection in square cavities filled with nanofluids under various temperature boundary conditions
Natural convection heat transfer phenomena in nanofluid-filled square cavities with various temperature boundary conditions are studied computationally. From electronic cooling to building ventilation systems, such phenomena have numerous practical applications, and accurate simulations are crucial for developing new designs. Towards that end, the Navier–Stokes equations of incompressible flows are considered with thermal coupling. The base fluid is pure water, the nanoparticles are copper (Cu), cupric oxide (CuO), or aluminum oxide (Al2O3), and the nanofluids are assumed to be homogeneous. It is well known that, in the standard finite element method framework, inappropriate selection of interpolation functions, e.g., (bi-)linear equal-order-interpolation velocity-pressure (e.g., and ) elements, yields nonphysical oscillations in the flow field for simulating incompressible flows, particularly for high Rayleigh numbers. In this study, in order to overcome such numerical instability issues, the streamline-upwind/Petrov–Galerkin (SUPG) and pressure-stabilizing/Petrov–Galerkin (PSPG) finite element formulations are utilized. The SUPG/PSPG-stabilized (SUPS) formulation is also enhanced with the least-squares on incompressibility constraint (LSIC). A comprehensive set of numerical test computations is considered for the values of the Rayleigh numbers ranging from to and a broad range of volume fractions of nanoparticles from to . Incompressible flow solvers are developed in-house and executed in parallel. Numerical simulations and comparisons with reported studies reveal that the proposed formulation performs quite well even at high Rayleigh numbers, and it does not exhibit any significant local or globally spread numerical instabilities. It is also noted that this is achieved without employing any adaptive mesh strategies and using only linear and equal-order interpolation functions, which in turn saves computational time.
期刊介绍:
International Communications in Heat and Mass Transfer serves as a world forum for the rapid dissemination of new ideas, new measurement techniques, preliminary findings of ongoing investigations, discussions, and criticisms in the field of heat and mass transfer. Two types of manuscript will be considered for publication: communications (short reports of new work or discussions of work which has already been published) and summaries (abstracts of reports, theses or manuscripts which are too long for publication in full). Together with its companion publication, International Journal of Heat and Mass Transfer, with which it shares the same Board of Editors, this journal is read by research workers and engineers throughout the world.