We continue our study of the transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence from non-equilibrium initial conditions to equilibrium using long-time numerical simulations on a 1283 periodic grid. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time. The six runs that previously went to near equilibrium are here extended into equilibrium. As before, we neglect dissipation as we are primarily concerned with behavior at the largest scale where this behavior has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. These six runs have various combinations of imposed rotation and mean magnetic field and represent the five cases of ideal, homogeneous, incompressible, and MHD turbulence: Case I (Run 1), with no rotation or mean field; Case II (Runs 2a and 2b), where only rotation is imposed; Case III (Run 3), which has only a mean magnetic field; Case IV (Run 4), where rotation vector and mean magnetic field direction are aligned; and Case V (Run 5), which has non-aligned rotation vector and mean field directions. Statistical mechanics predicts that dynamic Fourier coefficients are zero-mean random variables, but largest-scale coherent magnetic structures emerge and manifest themselves as Fourier coefficients with very large, quasi-steady, mean values compared to their standard deviations, i.e., there is ‘broken ergodicity.’ These magnetic coherent structures appeared in all cases during transition to near equilibrium. Here, we report that, as the runs were continued, these coherent structures remained quasi-steady and energetic only in Cases I and II, while Case IV maintained its coherent structure but at comparatively low energy. The coherent structures that appeared in transition in Cases III and V were seen to collapse as their associated runs extended into equilibrium. The creation of largest-scale, coherent magnetic structure appears to be a dynamo process inherent in ideal MHD turbulence, particularly in Cases I and II, i.e., those cases most pertinent to planets and stars. Furthermore, the statistical theory of ideal MHD turbulence has proven to apply at the largest scale, even when dissipation and forcing are included. This, along with the discovery and explanation of dynamically broken ergodicity, is essentially a solution to the ‘dynamo problem’.
我们继续研究理想的、均匀的、不可压缩的、磁流体动力学(MHD)湍流从非平衡初始条件到平衡的转变，使用1283周期网格上的长时间数值模拟。采用傅里叶谱变换方法对动力学方程进行时间正演数值积分。之前接近平衡的六次运行在这里延伸到平衡状态。和以前一样，我们忽略了耗散，因为我们主要关注的是在最大尺度上的行为，而这种行为已经被证明在理想和实际(强迫和耗散)MHD湍流中基本上是相同的。这六次运行具有施加旋转和平均磁场的不同组合，代表了理想、均匀、不可压缩和MHD湍流的五种情况:情况1(运行1)，没有旋转或平均场;情况II(运行2a和2b)，其中只施加旋转;情形III(运行3)，只有平均磁场;情形IV (Run 4)，旋转矢量与平均磁场方向对齐;Case V (Run 5)，它具有不对齐的旋转矢量和平均场方向。统计力学预测，动态傅里叶系数是零均值随机变量，但最大规模的相干磁结构出现并表现为傅里叶系数，其平均值与其标准差相比非常大，准稳定，即存在“破遍历性”。这些磁相干结构在过渡到接近平衡状态的所有情况下都出现了。在这里，我们报告说，随着运行的继续，这些相干结构只在情形1和情形2中保持准稳定和能量，而情形4保持其相干结构，但能量相对较低。在案例III和案例V中，在过渡时期出现的连贯结构随着其相关运行扩展到平衡状态而崩溃。最大规模的相干磁结构的产生似乎是理想MHD湍流所固有的一个发电机过程，特别是在情况I和II中，即与行星和恒星最相关的那些情况。此外，理想MHD湍流的统计理论已被证明适用于最大尺度，即使包括耗散和强迫。这与动态破缺遍历性的发现和解释一起，本质上是“发电机问题”的解决方案。
{"title":"Transition to Equilibrium and Coherent Structure in Ideal MHD Turbulence, Part 2","authors":"John V. Shebalin","doi":"10.3390/fluids8060181","DOIUrl":"https://doi.org/10.3390/fluids8060181","url":null,"abstract":"We continue our study of the transition of ideal, homogeneous, incompressible, magnetohydrodynamic (MHD) turbulence from non-equilibrium initial conditions to equilibrium using long-time numerical simulations on a 1283 periodic grid. A Fourier spectral transform method is used to numerically integrate the dynamical equations forward in time. The six runs that previously went to near equilibrium are here extended into equilibrium. As before, we neglect dissipation as we are primarily concerned with behavior at the largest scale where this behavior has been shown to be essentially the same for ideal and real (forced and dissipative) MHD turbulence. These six runs have various combinations of imposed rotation and mean magnetic field and represent the five cases of ideal, homogeneous, incompressible, and MHD turbulence: Case I (Run 1), with no rotation or mean field; Case II (Runs 2a and 2b), where only rotation is imposed; Case III (Run 3), which has only a mean magnetic field; Case IV (Run 4), where rotation vector and mean magnetic field direction are aligned; and Case V (Run 5), which has non-aligned rotation vector and mean field directions. Statistical mechanics predicts that dynamic Fourier coefficients are zero-mean random variables, but largest-scale coherent magnetic structures emerge and manifest themselves as Fourier coefficients with very large, quasi-steady, mean values compared to their standard deviations, i.e., there is ‘broken ergodicity.’ These magnetic coherent structures appeared in all cases during transition to near equilibrium. Here, we report that, as the runs were continued, these coherent structures remained quasi-steady and energetic only in Cases I and II, while Case IV maintained its coherent structure but at comparatively low energy. The coherent structures that appeared in transition in Cases III and V were seen to collapse as their associated runs extended into equilibrium. The creation of largest-scale, coherent magnetic structure appears to be a dynamo process inherent in ideal MHD turbulence, particularly in Cases I and II, i.e., those cases most pertinent to planets and stars. Furthermore, the statistical theory of ideal MHD turbulence has proven to apply at the largest scale, even when dissipation and forcing are included. This, along with the discovery and explanation of dynamically broken ergodicity, is essentially a solution to the ‘dynamo problem’.","PeriodicalId":12397,"journal":{"name":"Fluids","volume":"77 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135961472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Clément Loiseau, Stéphane Mimouni, Didier Colmont, Stéphane Vincent
The CFD numerical study of the flash boiling phenomenon of a water film was conducted using an Euler–Euler method, and compared to the experiments on the flashing of a water film. The water film is initially heated at temperatures ranging from 34 to 74 ∘C (frim 1 to 41 ∘C superheat), and the pressure is decreased from 1 bar to 50 mbar during the experiments. This paper shows that the experiments could not be correctly modelled by a simple liquid/bubble model because of the overestimation of the drag force above the water film (in the gas/droplet region). The generalised large interface model (GLIM), however, a multi-regime approach implemented in the version 7.0 of the neptune_cfd software, is able to differentiate the water film, where liquid/bubble interactions are predominant from the gas region where gas/droplet interactions are predominant, and gives nice qualitative results. Finally, this paper shows that the interfacial heat transfer model of Berne for superheated liquids could accurately predict the evolution of the water temperature over time.
{"title":"Numerical Modelling of Water Flashing at Sub-Atmopsheric Pressure with a Multi-Regime Approach","authors":"Clément Loiseau, Stéphane Mimouni, Didier Colmont, Stéphane Vincent","doi":"10.3390/fluids8050143","DOIUrl":"https://doi.org/10.3390/fluids8050143","url":null,"abstract":"The CFD numerical study of the flash boiling phenomenon of a water film was conducted using an Euler–Euler method, and compared to the experiments on the flashing of a water film. The water film is initially heated at temperatures ranging from 34 to 74 ∘C (frim 1 to 41 ∘C superheat), and the pressure is decreased from 1 bar to 50 mbar during the experiments. This paper shows that the experiments could not be correctly modelled by a simple liquid/bubble model because of the overestimation of the drag force above the water film (in the gas/droplet region). The generalised large interface model (GLIM), however, a multi-regime approach implemented in the version 7.0 of the neptune_cfd software, is able to differentiate the water film, where liquid/bubble interactions are predominant from the gas region where gas/droplet interactions are predominant, and gives nice qualitative results. Finally, this paper shows that the interfacial heat transfer model of Berne for superheated liquids could accurately predict the evolution of the water temperature over time.","PeriodicalId":12397,"journal":{"name":"Fluids","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136000472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The two-fluid (Euler–Euler) model and large-eddy simulation are used to compute the turbulent two-phase flow of air and water in a cyclonic flotation device known as an Air-Sparged Hydrocyclone (ASH). In the operation of ASH, air is injected through a porous cylindrical wall. The study considers a 48 mm diameter hydrocyclone and uses a block-structured fine mesh of 10.5 million hexagonal elements. The air-to-water injection ratio is 4, and a uniform air bubble diameter of 0.5 mm is specified. The flow field in ASH was investigated for the inlet flow rate of water of 30.6 L/min at different values of underflow exit pressure. The current simulations quantify the effects of the underflow exit pressure on the split ratio and the overall flow physics in ASH, including the distribution of the air volume fraction, water axial velocity, tangential velocity, and swirling-layer thickness. The loci of zero-axial velocity surfaces were determined for different exit pressures. The water split ratio through the overflow opening varies with underflow exit pressure as 6%, 8%, 16%, and 26% for 3, 4, 5, and 6 kPa, respectively. These results indicate that regulating the pressure at the underflow exit can be used to optimize the ASH’s performance. Turbulent energy spectra in different regions of the hydrocyclone were analyzed. Small-scale turbulence spectra at near-wall points exhibit f−4 law, where f is frequency. Whereas for points at the air-column interface, the energy spectra show an inertial subrange f−5/3 followed by a dissipative range of f−7 law.
{"title":"Two-Fluid Large-Eddy Simulation of Two-Phase Flow in Air-Sparged Hydrocyclone","authors":"Mustafa Bukhari, Hassan Fayed, Saad Ragab","doi":"10.3390/fluids8050139","DOIUrl":"https://doi.org/10.3390/fluids8050139","url":null,"abstract":"The two-fluid (Euler–Euler) model and large-eddy simulation are used to compute the turbulent two-phase flow of air and water in a cyclonic flotation device known as an Air-Sparged Hydrocyclone (ASH). In the operation of ASH, air is injected through a porous cylindrical wall. The study considers a 48 mm diameter hydrocyclone and uses a block-structured fine mesh of 10.5 million hexagonal elements. The air-to-water injection ratio is 4, and a uniform air bubble diameter of 0.5 mm is specified. The flow field in ASH was investigated for the inlet flow rate of water of 30.6 L/min at different values of underflow exit pressure. The current simulations quantify the effects of the underflow exit pressure on the split ratio and the overall flow physics in ASH, including the distribution of the air volume fraction, water axial velocity, tangential velocity, and swirling-layer thickness. The loci of zero-axial velocity surfaces were determined for different exit pressures. The water split ratio through the overflow opening varies with underflow exit pressure as 6%, 8%, 16%, and 26% for 3, 4, 5, and 6 kPa, respectively. These results indicate that regulating the pressure at the underflow exit can be used to optimize the ASH’s performance. Turbulent energy spectra in different regions of the hydrocyclone were analyzed. Small-scale turbulence spectra at near-wall points exhibit f−4 law, where f is frequency. Whereas for points at the air-column interface, the energy spectra show an inertial subrange f−5/3 followed by a dissipative range of f−7 law.","PeriodicalId":12397,"journal":{"name":"Fluids","volume":"95 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135068187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The supersonic flow of a reactive gas mixture with Mach reflection of oblique shocks and pulsed energy supply at the Mach stem is considered within the framework of the Chapman–Jouguet theory. An approximate analytical model is proposed that quickly determines the shape and size of the shock-wave structure as well as the flow parameters in various flow regions. As an example of the application of the proposed analytical model, the “first barrel” of a highly overexpanded jet flow of an air-methane mixture with a high supersonic velocity, is studied. Flows of hydrogen–air and hydrogen–oxygen mixtures were also considered for comparison with preceding numerical results. The height of the triple point of the Mach reflection is determined in the presence of a change in the chemical composition of the mixture and an isobaric pulsed energy supply at the main shock.
{"title":"An Approximate Analytical Model of a Jet Flow with Mach Reflection and Pulsed Energy Supply at the Main Shock","authors":"Mikhail V. Chernyshov, Karina E. Savelova","doi":"10.3390/fluids8040132","DOIUrl":"https://doi.org/10.3390/fluids8040132","url":null,"abstract":"The supersonic flow of a reactive gas mixture with Mach reflection of oblique shocks and pulsed energy supply at the Mach stem is considered within the framework of the Chapman–Jouguet theory. An approximate analytical model is proposed that quickly determines the shape and size of the shock-wave structure as well as the flow parameters in various flow regions. As an example of the application of the proposed analytical model, the “first barrel” of a highly overexpanded jet flow of an air-methane mixture with a high supersonic velocity, is studied. Flows of hydrogen–air and hydrogen–oxygen mixtures were also considered for comparison with preceding numerical results. The height of the triple point of the Mach reflection is determined in the presence of a change in the chemical composition of the mixture and an isobaric pulsed energy supply at the main shock.","PeriodicalId":12397,"journal":{"name":"Fluids","volume":"140 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135034176","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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