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Recent progress on the jetting of single deformed cavitation bubbles near boundaries 边界附近单个变形空化气泡喷射的最新进展
IF 2.5 3区 工程技术 Pub Date : 2023-12-12 DOI: 10.1007/s42241-023-0071-6
Jing-zhu Wang, Guang-hang Wang, Qing-yun Zeng, Yi-wei Wang

Cavitation occurs widely in nature and engineering and is a complex problem with multiscale features in both time and space due to its associating violent oscillations. To understand the important but complicated phenomena and fluid mechanics behind cavitation, a great deal of effort has been invested in investigating the collapse of a single bubble near different boundaries. This review aims to cover recent developments in the collapse of single bubbles in the vicinity of complex boundaries, including single boundaries and two parallel boundaries, and open questions for future research are discussed. Microjets are the most prominent features of the non-spherical collapse of cavitation bubbles near boundaries and are directed toward rigid walls and away from free surfaces. Such a bubble generally splits, resulting in the formation of two axial jets directed opposite to each other under the constraints of an elastic boundary or two parallel boundaries. The liquid jet penetrates the bubble, impacts the boundary, and exerts a great deal of stress on any nearby boundary. This phenomenon can cause damage, such as the erosion of blades in hydraulic machinery, the rupture of human blood vessels, and underwater explosions, but can also be exploited for applications, such as needle-free injection, drug and gene delivery, surface cleaning, and printing. Many fascinating developments related to these topics are presented and summarized in this review. Finally, three directions are proposed that seem particularly fruitful for future research on the interaction of cavitation bubbles and boundaries.

空化现象广泛存在于自然界和工程领域,由于其伴随的剧烈振荡,它是一个在时间和空间上都具有多尺度特征的复杂问题。为了理解空化背后重要而复杂的现象和流体力学,人们投入了大量精力研究不同边界附近单个气泡的坍塌。本综述旨在介绍复杂边界(包括单一边界和两个平行边界)附近单个气泡坍缩的最新研究进展,并讨论未来研究的开放性问题。微射流是空化气泡在边界附近非球形塌陷的最显著特征,它朝向刚性壁,远离自由表面。这种气泡一般会分裂,在弹性边界或两个平行边界的限制下形成两个方向相反的轴向射流。液体射流穿透气泡,冲击边界,并对附近的任何边界施加很大的应力。这种现象会造成损害,如液压机械叶片的侵蚀、人体血管的破裂和水下爆炸,但也可用于各种应用,如无针注射、药物和基因输送、表面清洁和打印。本综述介绍并总结了与这些主题相关的许多引人入胜的发展。最后,本文提出了三个方向,这三个方向似乎是空化气泡与边界相互作用未来研究的主要方向。
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引用次数: 0
A numerical study of hydrodynamic characteristics and hydrological processes in the coastal wetlands during extreme events 极端事件期间沿海湿地水动力特征和水文过程的数值研究
IF 2.5 3区 工程技术 Pub Date : 2023-12-12 DOI: 10.1007/s42241-023-0072-5
Ming-liang Zhang, Xiao-sen Zhu, Yu-jia Wang, Heng-zhi Jiang, Lei Cui

Providing accurate predictions of extreme water levels through numerical simulation has become essential for disaster prevention and damage mitigation in coastal wetland areas. This study applies the FVCOM model to simulate storm surges caused by several typhoons in the Bohai Sea and the North Huanghai Sea. The vegetation drag force caused by salt marsh plants is inserted into the FVCOM model for model improvement with vegetation effect by integrating RS and GIS technologies. A parametric typhoon model is coupled with background wind fields derived to acquire the spatio-temporal variations of wind and pressure fields in the computational domain. The simulation results reproduce the extreme storm surges induced by typhoon events very well. The modeling results are compared by validating with literature results to examine the effect of vegetation on tidal waves in tidal mud flats. Moreover, the coupled model is also applied to explore storm surge attenuation and land intrusion during Typhoon Winnie in the wetlands of the Liao River Estuary. The simulation results indicate that salt marsh plants can reduce the flow current with little impact on tide flooding/ebbing in vegetated regions. Furthermore, the results show that typhoon presence increases the inundation depth and extendes the flood time in the tidal wetlands of the study region. The FVCOM model incorporating the method with vegetation drag force can provide new insights to understand the comprehensive impact of tidal wetland plants on hydrodynamic characteristics in the Bohai Sea and other waters, hence presents a more accurate quantification of the hydrological process of storm surge in the tidal wetlands.

通过数值模拟对极端水位进行准确预测对于沿海湿地地区的防灾减灾工作至关重要。本研究应用 FVCOM 模型模拟了渤海和黄海北部多个台风引起的风暴潮。在 FVCOM 模型中加入了盐沼植物引起的植被阻力,通过集成 RS 和 GIS 技术,利用植被效应对模型进行改进。台风参数模型与背景风场耦合,获取计算域内风场和气压场的时空变化。模拟结果很好地再现了台风事件引发的极端风暴潮。模拟结果与文献结果进行了对比验证,以研究植被对滩涂潮汐波的影响。此外,该耦合模型还被用于探讨台风 "温妮 "期间辽河口湿地的风暴潮衰减和陆地入侵问题。模拟结果表明,在植被覆盖的区域,盐沼植物可以减弱水流,而对潮水淹没/侵蚀的影响很小。此外,模拟结果表明,台风的存在增加了研究区域潮汐湿地的淹没深度,延长了淹没时间。结合植被阻力法的 FVCOM 模型可为了解渤海及其他水域潮汐湿地植物对水动力特性的综合影响提供新的见解,从而更准确地量化潮汐湿地风暴潮的水文过程。
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引用次数: 0
Entropy production by dissipation effects and characteristic vortex evolution in a rocket turbopump 火箭涡轮泵中耗散效应产生的熵和特征涡流演变
IF 2.5 3区 工程技术 Pub Date : 2023-12-12 DOI: 10.1007/s42241-023-0073-4
De-you Li, Jia-qi Zhu, Rui-yi Zhang, Yi Zhang, Zhi-peng Li, Hong-jie Wang, Zhi-peng Ren

The relationship between entropy production and vortex evolution affects the efficiency and stability of rotating machinery. This study investigated the energy characteristics of a rocket turbopump and revealed the correlated mechanisms of the entropy production rate using the dissipation effects and characteristic vortex evolution. For the first time, direct and turbulent dissipation and rigid and shear vorticity decomposition methods were utilized to analyze the correlation between flow loss and characteristic vorticities in rotating machinery. With an increase in the flow rate, the hydraulic losses of the dissipation effects and wall decreased by 60% and 38.3%, respectively, and the proportions of the input energy decreased (from 13% to 8%) and remained stable (8%), respectively. The local direct dissipative entropy production (DDEP) in the inducer-impeller is strongly related to shear entropy, and the correlated effect of total enstrophy on DDEP is weaker than that of shear vorticity, indicating that rigid enstrophy suppresses direct dissipation. The correlation between turbulent dissipation and rigid enstrophy was significantly weaker in the static flow passage of the turbopump owing to the weak rigid rotational effect. The correlation between the rigid entropy and local turbulent dissipative entropy production (TDEP) gradually increased with increasing flow rate, reaching a medium correlation (the maximal correlated degree in the turbopump) and exhibiting rigid rotation effects on the hydraulic loss. Moreover, the flow rate significantly affected the correlation (except for the diffuser), and the two characteristic vorticities reached a maximum at the designed flow rate owing to optimal efficiency and minimum hydraulic loss.

熵产生和涡流演变之间的关系影响着旋转机械的效率和稳定性。本研究对火箭涡轮泵的能量特性进行了研究,并利用耗散效应和特征涡旋演化揭示了熵产生率的相关机制。研究首次利用直接耗散和湍流耗散以及刚性和剪切涡度分解方法分析了旋转机械中流动损失与特征涡度之间的相关性。随着流速的增加,耗散效应和壁面的水力损失分别降低了 60% 和 38.3%,输入能量的比例分别降低(从 13% 降至 8% )和保持稳定(8%)。诱导器-叶轮中的局部直接耗散熵产生(DDEP)与剪切熵密切相关,总熵对 DDEP 的相关影响弱于剪切涡度,表明刚性熵抑制了直接耗散。在涡轮泵的静态流道中,由于刚性旋转效应较弱,湍流耗散与刚性熵之间的相关性明显减弱。刚性熵与局部湍流耗散熵(TDEP)之间的相关性随着流速的增加而逐渐增大,达到中等相关性(涡轮泵中的最大相关性),并表现出刚性旋转对水力损失的影响。此外,流量对相关性有明显影响(扩散器除外),并且由于效率最优和水力损失最小,两个特征涡度在设计流量下达到最大。
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引用次数: 0
Experimental study of the dynamics of a single cavitation bubble excited by a focused laser near the boundary of a rigid wall 刚性壁面边界附近聚焦激光激发单个空化气泡动力学的实验研究
IF 2.5 3区 工程技术 Pub Date : 2023-11-30 DOI: 10.1007/s42241-023-0069-0
Xiang-qing Zhang, Xiao-fei Zhang, Xu Qiu, Dan Gao, Yu-ning Zhang

Based on high-speed photographic experiments, this study presents a detailed qualitative and quantitative analysis of the dynamics of a single cavitation bubble near the boundary of a rigid wall in asymmetric settings. The main findings are reported as follows: (1) The non-sphericity of the bubble interface decreases with increasing spacing between the bubble and the boundary, and the asymmetry of the bubble becomes more significant with increasing asymmetry angle. (2) The motion mode of the bubble cluster in the second oscillation cycle can be divided into two typical modes depending on the direction of movement. (3) The angle between the oblique jet pointing towards the upper wall surface and the horizontal direction in the second oscillation cycle decreases as the dimensionless spacing decreases.

基于高速摄影实验,本文对非对称条件下刚性壁面边界附近单个空化气泡的动力学进行了详细的定性和定量分析。主要研究结果如下:(1)气泡界面的非球性随气泡与边界间距的增大而减小,而气泡的不对称性随不对称角的增大而增强。(2)气泡团在第二个振荡周期的运动模式根据运动方向可分为两种典型模式。(3)在第二振荡周期中,指向上壁面的斜射流与水平方向的夹角随着无量纲间距的减小而减小。
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引用次数: 0
Numerical study on the aerodynamic and hydrodynamic performances of an ultra-high-speed AAMV 超高速AAMV气动与水动力性能数值研究
IF 2.5 3区 工程技术 Pub Date : 2023-11-30 DOI: 10.1007/s42241-023-0070-7
Qi-jun Ni, Shi-jun Ji, Yi Jiang, Sheng-zhong Li, Yang Liu, Wei-tong Xu

In order to investigate the resistance performance of an ultra-high-speed aerodynamically alleviated marine vehicle (AAMV), finite volume method (FVM)-based computational fluid dynamics (CFD) software STAR CCM+ is used to simulate the forward motion of this vehicle. The calculated results are validated as they reach good agreement with experimental data. Comparing the motions of models with and without aero-wings, the hybrid aerodynamic and hydrodynamic mechanism of this novel hull is discussed. Study is subsequently performed that how step configuration, spray rail and deadrise angle act on hull behavior and resistance. The results show that models with double steps and spray rail possess better resistance characteristics at high speeds, and planing surface with variable deadrise angle could further improve the overall navigation performance.

为了研究超高速空气动力学缓和船舶(AAMV)的阻力性能,采用基于有限体积法(FVM)的计算流体动力学(CFD)软件STAR CCM+对该船舶的正向运动进行了模拟。计算结果与实验数据吻合较好,得到了验证。比较了带翼和不带翼模型的运动,讨论了这种新型船体的气动和水动力混合机理。随后,研究了阶梯结构、喷淋导轨和死升角对船体性能和阻力的影响。结果表明,采用双台阶和喷雾导轨的模型在高速下具有更好的阻力特性,采用可变死升角的平面可以进一步提高整体导航性能。
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引用次数: 0
Induced noise of impeller stuck and passive rotation state in multi-stage pump without power drive under natural flow conditions 无动力驱动多级泵在自然流动条件下叶轮卡滞和被动转动状态引起的噪声
IF 2.5 3区 工程技术 Pub Date : 2023-11-30 DOI: 10.1007/s42241-023-0068-1
Run-ze Zhou, Hou-lin Liu, Ru-nan Hua, Liang Dong, Kim Tiow Ooi, Cui Dai, Si-yuan Hu

The natural flow cooling strategy is commonly employed in modern high-speed vessels and nuclear-powered submarines. These vessels rely on the energy generated by their own speed to drive the cooling system and supply cooling water to the condenser. The circulating pump, which operates without a motor drive under natural flow conditions, is a large resistance component in the cooling system. However, it is also the primary noise source, significantly impacting the vessel’s safe operation and acoustic stealth performance. This study investigates the induced noise characteristics of a multi-stage pump under natural flow conditions by experiment, computational fluid dynamics (CFD), and acoustic finite element method. The analysis encompasses the distribution of the flow field, variations in acoustic power, spectral features of flow-induced noise, and directivity of external field radiation noise under different natural flow conditions. The results show that the acoustic power distribution is correlated with the flow field. When the impeller is stuck, the noise sources primarily concentrate in the flow separation area at the blade’s leading edge, the interface area between the impeller and the guide vane, and the flow shock area inside the guide vane. Conversely, when the impeller rotates passively, the blade wake area has a higher acoustic power. The flow noise spectrum under natural flow conditions mainly exhibits broadband and discrete characteristics. Additionally, the pump structure influences the external field radiation noise, and its directivity varies with different flow rates and characteristic frequencies. This study provides valuable insights into optimal design to reduce the noise of the circulating pump in the vessel’s natural flow cooling system. It is essential for ensuring the safe operation and acoustic stealth performance of high-speed vessels and nuclear-powered submarines.

现代高速船舶和核动力潜艇普遍采用自然流冷却策略。这些容器依靠自身速度产生的能量来驱动冷却系统,并为冷凝器提供冷却水。循环泵是冷却系统中阻力较大的部件,在自然流动条件下无需电机驱动即可运行。然而,它也是主要噪声源,严重影响船舶的安全运行和声隐身性能。采用实验、计算流体力学(CFD)和声学有限元等方法研究了多级泵在自然流动条件下的诱导噪声特性。分析了不同自然流动条件下的流场分布、声功率变化、流致噪声的频谱特征以及外场辐射噪声的指向性。结果表明,声功率分布与流场有关。当叶轮卡滞时,噪声源主要集中在叶片前缘的流动分离区、叶轮与导叶的界面区以及导叶内部的流动激波区。反之,当叶轮被动旋转时,叶片尾迹区声功率更高。自然流动条件下的流动噪声谱主要表现为宽频和离散特征。此外,泵的结构还会影响外场辐射噪声,其指向性随流量和特征频率的不同而变化。该研究为船舶自然流冷却系统中循环泵噪声的优化设计提供了有价值的见解。它对保证高速舰船和核动力潜艇的安全运行和声隐身性能至关重要。
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引用次数: 0
Numerical study on the wave pattern characteristic of air layer in cavity and the effects of multiple influence factors 空腔内空气层波型特征及多种影响因素影响的数值研究
IF 2.5 3区 工程技术 Pub Date : 2023-11-23 DOI: 10.1007/s42241-023-0066-3
Xiao-song Zhang, Xue-qin Ji, Lei-qiang Chen, Li-jin Gao, Hong-bo Huang, Fang-wen Hong

Air-layer drag reduction (ALDR) technology for ship energy saving is getting more and more attention in recent years because of the outstanding drag reduction effect. In order to promote practical application, it is necessary to fully understand the two phase flow characteristics of the air layer. Recent experimental studies have shown that the surface of the air layer presents wave pattern, which has an important influence on its damage risk. However, it is difficult to measure the wave pattern quantificationally due to the interference of equipment. The main goal of the present paper is to investigate the wave pattern characteristic of air layer in cavity using numerical simulation method. On this basis, the effect of flow and geometric influence factors are discussed to understand the key control conditions. A computational fluid dynamics (CFD) numerical method based on Reynolds averaged Navier-Stokes (RANS) equations and volume of fluid (VOF) interface capturing method is established, and has been successfully applied in the simulation of air layer wave pattern. Both 2-D and 3-D simulations are carried out, aiming at analyzing air-water interface flow and vortex flow directly. Based on the simulation results, several important conclusions about the mechanism of air layer wave pattern can be obtained. Firstly, it is found to be an inherent characteristic that the wave height of the upstream air layer is higher than that of the downstream. The extremely high wave peak is easy to contact with the flat plate, leading to the breakup of air layer and a “central blank area” phenomenon. With the help of flow analysis, it is found that this characteristic is mainly caused by the strong counterclockwise vortex behind the bow wedge block. Secondly, the air layer stability is reduced with the increase of water flow velocity by affecting the wave height. There is a saturation point of air flow rate to reach maximum thickness of air layer. Thirdly, cavity configuration has obvious influence on air layer stability by influencing vortex flow field. The increase of cavity depth and width can aggravate the unsteady and nonlinear characteristics of air layer. Finally, comprehensive design criteria are concluded from the view of geometrical configuration and flow conditions. A cavity with the moderate depth and width can avoid the upstream damage of air layer. Longitudinal position of air nozzles should be set within the low pressure zone behind the wedge block for stable air layer formation.

近年来,船舶空气层减阻技术因其显著的减阻效果而受到越来越多的关注。为了促进实际应用,有必要充分了解空气层的两相流动特性。近年来的实验研究表明,空气层表面存在波型,这对其损伤风险有重要影响。然而,由于设备的干扰,对波形进行定量测量是困难的。本文的主要目的是利用数值模拟方法研究空腔中空气层的波型特征。在此基础上,讨论了流量和几何影响因素的作用,了解了关键控制条件。建立了基于Reynolds平均Navier-Stokes (RANS)方程和流体体积(VOF)界面捕获法的计算流体力学(CFD)数值方法,并成功应用于空气层波型的模拟。为了直接分析空气-水界面流动和涡旋流动,进行了二维和三维模拟。根据模拟结果,得出了关于空气层波型形成机理的几个重要结论。首先,发现上游空气层波高高于下游空气层波高是其固有特征。极高的波峰容易与平板接触,导致空气层破裂,出现“中心空白区”现象。通过流动分析发现,这种特性主要是由弓形楔块后强烈的逆时针涡引起的。其次,随着水流速度的增加,空气层的稳定性通过影响波高而降低。空气流速存在饱和点,达到最大空气层厚度。第三,空腔形态通过影响涡旋流场对空气层稳定性有明显影响。空腔深度和宽度的增加会加剧空气层的非定常和非线性特性。最后从几何形态和流动条件两方面总结了综合设计准则。适当深度和宽度的空腔可以避免空气层的上游破坏。喷嘴的纵向位置应设置在楔块后面的低压区内,以稳定空气层的形成。
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引用次数: 0
Research on the collapse process of a near-wall bubble 近壁气泡崩塌过程的研究
IF 2.5 3区 工程技术 Pub Date : 2023-11-23 DOI: 10.1007/s42241-023-0067-2
Bing Zhu, Wang Han, Wen-jun Xu, Wei Zhang

The effect of wall on the bubble collapse is significant. A compressible numerical simulation method based on the state equation was used to numerically calculate the collapse process of bubbles at different leaving wall distances. The results show that when the dimensionless distance between the bubble center and the wall is greater than zero, the bubble generates a high-pressure region at the top of the interface, which induces a jet toward the wall. When the dimensionless distance is less than zero, the jet is generated from the vicinity of the contact position between the bubble and the wall and moves along the wall towards the center axis of the bubble. When the dimensionless distance is equal to zero, that is, the center of the bubble coincides with the center of the wall, the bubble shrinks uniformly, and its collapse process is consistent with that of a single bubble in free space under the same parameter conditions. Comparison of these three typical cases of dimensionless distance from the wall reveals that the presence of the wall induces an asymmetric effect and a pressure gradient effect in the flow field around the bubble, and the farthest point away from the center of the attached wall is a high-pressure region, which induces destabilization of the bubble interface and the occurrence of jets.

壁面对气泡破裂的影响是显著的。采用基于状态方程的可压缩数值模拟方法,对气泡在不同离壁距离下的崩塌过程进行了数值计算。结果表明:当气泡中心与壁面的无因次距离大于零时,气泡在界面顶部形成一个高压区,该高压区诱导射流向壁面方向运动;当无量纲距离小于零时,射流从气泡与壁面接触位置附近产生,并沿壁面向气泡中心轴方向运动。当无量纲距离为零,即气泡中心与壁面中心重合时,气泡均匀收缩,其坍缩过程与相同参数条件下自由空间中单个气泡的坍缩过程一致。通过与壁面无量纲距离的三种典型情况的对比可知,壁面的存在在气泡周围的流场中产生了不对称效应和压力梯度效应,离壁面中心最远的地方是一个高压区,这导致了气泡界面的失稳和射流的产生。
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引用次数: 0
Influence of bubble-particle distance on the dynamic behaviors of a cavitation bubble near a particle 气泡-粒子距离对粒子附近空化气泡动力学行为的影响
IF 2.5 3区 工程技术 Pub Date : 2023-11-16 DOI: 10.1007/s42241-023-0063-6
Yun Dai, Hui Zhang, Ting Chen

Cavitation and silt-erosion often co-exist, causing severe damage on fluid machinery. In this paper, the dynamic behavior of a cavitation bubble near a fixed spherical particle is numerically studied, with the focus on the influence of the stand-off distance γ on the bubble collapse morphology, micro-jet velocities and pressure on the particle. With the increase in the value of γ, the bubble profile in the collapse stage exhibits three distinct characteristics: Mushroom-shaped, pear-shaped and spherical-shaped, and the corresponding micro-jets are identified as contact jet, non-contact jet, and long-distance jet. All studied distances can be categorized into three ranges, and the typical cases in each range are demonstrated. The maximum jet velocity Vmax and the maximum pressure difference between the upper and the bottom of the particle Δpmax show the highest peak at γ = 0.9, with Vmax up to 180 m/s and Δpmax up to 10.8 MPa.

空化和泥沙侵蚀经常并存,对流体机械造成严重的破坏。本文采用数值方法研究了固定球形颗粒附近空化气泡的动力学行为,重点研究了离空距离γ对气泡破裂形态、微射流速度和颗粒压力的影响。随着γ值的增大,崩溃阶段的气泡轮廓呈现出蘑菇形、梨形和球形三个明显特征,相应的微射流可分为接触射流、非接触射流和远距离射流。所有研究的距离可以分为三个范围,并在每个范围内展示了典型案例。最大射流速度Vmax和颗粒上下最大压差Δpmax在γ = 0.9处达到峰值,Vmax可达180 m/s, Δpmax可达10.8 MPa。
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引用次数: 0
CFD simulations targeting the performance of the NTNU BT1 wind turbine using overset grids 针对NTNU BT1风力机性能的过置网格CFD模拟
IF 2.5 3区 工程技术 Pub Date : 2023-11-16 DOI: 10.1007/s42241-023-0065-4
Mao-kun Ye, Ni-na Wang, Hamn-Ching Chen, De-cheng Wan

In the present study, the performance of the NTNU Blind Test 1 wind turbine is analyzed in the computational fluid dynamics (CFD) simulations by using the CFD code FANS with structured overset grids. First, the numerical methods including the governing equations, the turbulence closure model, and the flow solver are introduced. In addition, the NTNU BT1 wind tunnel experiment is described. Then, structured overset grid blocks are generated in the computational domain with fully resolved wind turbine geometry, including the blades, hub, nacelle, and tower. Afterward, unsteady Reynolds averaged Navier-Stokes (RANS) simulations with the two-layer k - ε turbulence model are performed with an inlet velocity of 10 m/s and a tip-speed ratio (TSR) of 6. The overset-grid capability of FANS is leveraged to handle the rotation of the rotor. Finally, simulations are performed for a range of TSRs and a comparison is made among the present CFD results, other numerical results obtained from representative methods, and the experimental data. It is observed that the CFD-predicted thrust coefficients match the experimental measurement at low TSRs while under-predicting the values at high TSRs, and potential reasons for this deviation are discussed.

在计算流体力学(CFD)模拟中,采用结构过置网格计算流体力学(CFD)程序FANS对NTNU盲测1型风力机的性能进行了分析。首先介绍了控制方程、湍流闭合模型和流场求解等数值方法。此外,还介绍了NTNU BT1风洞试验。然后,在计算域中生成具有完全解析的风力涡轮机几何形状的结构化重叠网格块,包括叶片、轮毂、机舱和塔。在进口速度为10 m/s、叶尖速比(TSR)为6的条件下,采用两层k - ε湍流模型进行了非定常Reynolds平均Navier-Stokes (RANS)模拟。利用风扇的过电网能力来处理转子的旋转。最后,对一定范围内的tsr进行了数值模拟,并将本文计算结果与其他代表性方法的数值结果与实验数据进行了比较。观察到cfd预测的推力系数在低tsr时与实验测量值相符,而在高tsr时预测不足,并讨论了这种偏差的可能原因。
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引用次数: 0
期刊
Journal of Hydrodynamics
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