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Numerical simulation of momentum transport processes through gas-liquid interface
https://ir.soken.ac.jp/records/512
https://ir.soken.ac.jp/records/512b62e4f8d-cb03-4e9d-b85a-c3e1a901d635
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要旨・審査要旨 (504.5 kB)
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本文 (3.8 MB)
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| Item type | 学位論文 / Thesis or Dissertation(1) | |||||
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| 公開日 | 2010-02-22 | |||||
| タイトル | ||||||
| タイトル | Numerical simulation of momentum transport processes through gas-liquid interface | |||||
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| タイトル | Numerical simulation of momentum transport processes through gas-liquid interface | |||||
| 言語 | en | |||||
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| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源タイプ識別子 | http://purl.org/coar/resource_type/c_46ec | |||||
| 資源タイプ | thesis | |||||
| 著者名 |
阿部, 陽介
× 阿部, 陽介 |
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| フリガナ |
アベ, ヨウスケ
× アベ, ヨウスケ |
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| 著者 |
ABE, Yousuke
× ABE, Yousuke |
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| 学位授与機関 | ||||||
| 学位授与機関名 | 総合研究大学院大学 | |||||
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| 学位名 | 博士（理学） | |||||
| 学位記番号 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | 総研大甲第838号 | |||||
| 研究科 | ||||||
| 値 | 物理科学研究科 | |||||
| 専攻 | ||||||
| 値 | 10 核融合科学専攻 | |||||
| 学位授与年月日 | ||||||
| 学位授与年月日 | 2005-03-24 | |||||
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| 値 | 2004 | |||||
| 要旨 | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | Free-surface turbulent flows are ubiquitously found in the nature as well as in various industrial devices such as a chemical plant, not to mention the turbulence in rivers and oceans. A two-phase flow for a gas and a liquid with a distorted interface is one of the most common issues for free-surface turbulent flows, and, recently, has been much paid attention to in the field of environmental science, specifically, in the climate projection study. Interaction between Atmosphere and Ocean is a key issue in the climate projection because their interaction affects the global circulation as well as the local weather. At the Earth Simulator Center, a high-resolution (100m - 10km for horizontal) non-hydrodynamic Atmosphere-Ocean coupling model has been developed in order to simulate not only a global phenomenon, but also a local one, such as a typhoon which may bring a terrible disaster. In this high-resolution regime, however, no reliable method of evaluating physical quantities, such as the momentum, heat, and vapor, exchanged through the interface has been established. Therefore, it is necessary to investigate fundamental physical processes in gas-liquid flows with a free-surface.<br /> In previous studies on the gas-liquid flows with a free-surface, mainly explored was the liquid side turbulence near the interface on which no or very low shear flow condition was imposed. A direct numerical simulation (DNS) of free-surface flows with the coupled gas-liquid dynamics should be useful for understanding a gas-liquid interaction mechanism through a detailed analysis of turbulent statistics which can not be obtained by experiments. Nevertheless, only a few trials have been made because of the numerical difficulties in tracking a free-surface, such as the numerical diffusion and instability accompanied with the interface deformation. Since, in a high velocity range commonly seen in realistic free-surface flows, turbulent characteristics near a free-surface could be influenced by deformation of the free-surface due to wind shear, it is necessary to take into account the effects of the interface distortion in the DNS of the gas-liquid flow simulation.<br /> Various kinds of two-phase flow models have been developed such as the level-set method and the volume-of-fluid (VOF) method. Recently, Kunugi (1997) has developed a precise free-surface tracking algorithm for two-phase flows, that is, Multi-interfaces Advection and Reconstruction Solver (MARS). Yabe and Wang (1991) proposed the CIP-combined, unified procedure (C-CUP method) which can treat the compressible and incompressible fluids, simultaneously, in the same code. Even in cases that an interface is largely deformed by a strong wind shear, the C-CUP method can resolve the complicated interfaces on the Cartesian coordinates. Since it is not necessary to reconstruct the numerical grid in the C-CUP method, the numerical cost and errors can be reduced in comparison to MARS. Using the C-CUP method, Mutsuda et al. (1998, 1999) succeeded in performing a DNS of wave-breaking and entrained air bubble in a gas-liquid turbulent layer. However, there has been no quantitative evaluation of the friction stress by means of the two-phase flow simulation.<br /> The objective of this study is to show the validity of the numerical method based on the C-CUP scheme, by quantitatively comparing the simulation results with experimental data, towards construction of a reliable method for evaluating the friction stress between Atmosphere and Ocean. The reasons for adopting the C-CUP method are summarized as follows. First, applicability of the C-CUP method to the compressible fluid has an advantage in simulation of severe phenomena such as a typhoon. Second, the C-CUP method can keep thickness of a transition region near the sea-surface compact, which is important in long-term integration. Moreover, it is a more direct way to solve the same equations for both Atmosphere and Ocean, as is done in the C-CUP method, than separately treating them through boundary conditions on the sea-surface.<br /> In this study, the two-phase flow simulations for a gas and a liquid are performed with a numerical setting as given bellow. Setting of the numerical domain is relevant to tank-experiments. Turbulent Reynolds number Re<SUB>γ</SUB> is changed from 150 to 300 in order to find the wind velocity dependence of the friction. An effect of the water depth on evaluation of the friction velocity is also studied. In the deeper case, the water depth is relevant to that of the tank-experiments. The wind velocity is in a regime that the free-surface deformation accompanied with ripples can not be ignored, and is comparable to the representative velocity range in the tank-experiments. The continuum surface force (CSF) model, which is often used in two-phase flow simulations, proposed by Brackbill et al. (1992) is applied to the surface tension. In a transition region near the free-surface, the viscous coefficient is modeled by an inversely proportional relation which shows a better property than the linear relation and agrees with experimental data for two-phase mixing fluids by McAdams et al. (1942). In addition to the C-CUP method, the present simulation code is implemented with the following schemes in order to improve the numerical stability and accuracy in the high velocity range. The rational CIP method proposed by Xiao et al. (1996) can avoid negative values of the density and pressure in the transition region near the free-surface. The tangent transformed density function, which defines the transition region, proposed by Yabe and Xiao (1993) can reduce the numerical diffusion of the transition region keeping the compactness.<br /> From the statistical analysis of turbulence in the simulation results, we have quantitatively discussed the turbulent structures near the free-surface and the mechanism of the momentum transfer through the gas-liquid interface. The results obtained from the present simulation study on the two-phase flow, are summarized below.<br /> It is shown that the vertical velocity fluctuations normal to the free-surface are induced on the liquid side near the interface. To explain this behavior, we have made analysis of the pressure-strain correlation term that remains finite only near the free-surface on the liquid side. The surface-normal component of the pressure-strain correlation term has a positive value while the streamwise component is negative. This behavior indicates that the turbulent energy on the gas side is redistributed mainly into the vertical component of the velocity fluctuations on the liquid side through the free-surface deformations which are excited by the shear stress. Moreover, the result that all vorticity components increase near the free-surface shows the presence of three-dimensional turbulent structures. Thus, it is necessary to take into account the effects of the free-surface deformation on the momentum transfer process through the gas-liquid interface when a large shear stress exists. It is also suggested that the vertical velocity component should be accurately calculated, although the conventional numerical simulations have treated the velocity fields near the free-surface as almost two-dimensional.<br /> The turbulent structures are similar to those of the experiment, in which the representative wind velocity is almost the same as that of the present study. The Reynolds stress distribution is correlated with the free-surface structure. This result reflects that the momentum transfer through the gas-liquid interface is related to the Reynolds stress produced by the vertical velocity fluctuations near the free-surface. In order to verify the correlation, we have investigated a phase relation between a time series of the Reynolds stress on the gas side and that of the free-surface position. According to this analysis, large positive spikes of the Reynolds stress, which enhance the downward momentum transfer, often appear at positions where the 'burst' and the 'sweep' are observed. It is also consistent with the experiments. In addition, bursts of the Reynolds stress are observed in close to the crest over the windward side, as reported in the experiment. This agreement suggests that the present simulation captures the bursting phenomena produced by the Reynolds stress in relation to ordered motions such as the wind flow separation and the reattachment over wind waves. Therefore, it is considered that the momentum transfer process with the free-surface deformation can be well reproduced by the present DNS of the two-phase flow.<br /> The friction velocities are evaluated from the peak values of the friction stresses near the free-surface on the liquid side. The relation between the friction velocity and the mean velocity on the gas side is in good agreement with the tank-experimental data for both cases of the Reynolds numbers of 150 and 300. Especially, a better agreement is found for the deeper water condition. In the velocity range considered here, the free-surface deformation can not be ignored in contrast to the conditions for the conventional DNS studies, where the liquid turbulence is decoupled from the gas dynamics by supposing a flat interface and applying the free-slip condition. Therefore, the present study presents the first quantitative evaluation of the friction stresses on the free-surface, which is validated by a comparison with the tank experimental data.<br /> The three-second power law and the spectrum form of wind waves proposed by Toba (1972) are also examined for the case of the present numerical simulation. The form of the energy spectrum of wind waves is derived from a combination of the three-second power law and the similarity of the spectral form of wind waves. These are well substantiated by data from a wind-wave tunnel experiment. The three-second power law is obtained from the spectrum of wind waves based on the local balance between the wind waves and both the turbulent structures of the air and liquid flows. The period and the wave height of significant waves in dimensionless forms, which are considered to correspond to the peak frequency and the energy level, respectively, are used as representative quantities of wind waves. From the results of the present study, it is confirmed that the relation of the period and the height of significant waves is consistent to the three-second power law within the error coming from the wind-wave tunnel experiment and the field observation. In the gravity wave range, the spectral form on the high frequency side is proportional to the -4 power of the angular frequency of wind waves. The wind waves grow in a way that on the logarithmic diagram of the spectral density versus the angular frequency, the spectrum slides up along the line of the form, keeping its similar form. It is confirmed that the spectral density obtained by the present simulations has the -4 power of the angular frequency. The spectrum level shows a better agreement with the data of the wind-wave tunnel experiment than that of the field observation. The result suggests that the present numerical simulation can accurately represent the developing phase of wind waves in wind-wave tunnel experiments. As the wave number becomes large, the effect of surface tension is incorporated. Thus, the -4 power line found in the gravity wave range gradually approaches the -8/3 power line for the capillary wave range, which is also reproduced by the present simulations.<br /> The obtained results confirm that the present simulation method has a possibility of extension to a larger gas-liquid flow system towards construction of a reliable scheme for evaluating the friction stress between Atmosphere and Ocean. | |||||
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