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上海交通大学 船舶海洋与建筑工程学院, 海洋工程国家重点实验室, 高新船舶与深海开发装备协同创新中心,上海 200240
NUMERICAL SIMULATION OF LIQUID SLOSHING IN LNG TANK USING GPU-ACCELERATED MPS METHOD1)
ChenXiang, WanDecheng![](https://lxxb.cstam.org.cn/fileLXXB/richhtml/0459-1879/rich_nlm3_0/images/REemail.gif)
中图分类号:O35,U633
文献标识码:A
通讯作者:
收稿日期:2018-12-5
网络出版日期:2019-05-18
版权声明:2019力学学报期刊社 所有
基金资助:
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引 言
液舱晃荡是指在外部激励作用下部分装载的液舱内液体所产生的波动现象,其特征是自由液面的大幅度变形和强非线性破碎.随着世界能源需求的不断增加,许多运输液化天然气和石油的船舶纷纷建成.当这些部分装载的液货船在海上航行时,舱内运输的流体会产生晃荡,这将对舱室结构强度和船舶运行安全产生巨大的危害.因此,许多研究人员对液舱晃荡的机理特性开展了研究.Faltinsen[1]最早推导出了在水平激励作用下的二维液舱晃荡的解析解.Nakayama和Washizu[2-3]分别用有 限元方法和边界元方法分析了二维液舱晃荡问题.Kim等[4]采用标记网格法对二维和三维薄膜型液舱的晃荡问题进行了模拟,并分析了各参数对计算结果产生的影响.Zhu等[5]应用改进的等值面函数法对大幅度液舱晃荡的波高和砰击压力进行了准确的预报.Xue和Lin[6]采用流体体积法模拟了三维矩形液舱的晃荡问题,并对环形隔板的减晃效果进行了分析.虽然在液舱晃荡问题中,网格类方法已经取得了许多成果,但在处理强非线性变化的自由液面时仍有一定的困难,如波浪破碎、自由面翻卷等.无网格粒子类方法基于拉格朗日方法描述,粒子之间不存在固定的拓扑关系,能够很方便地模拟物体和自由液面的非线性变形[7-9].在液舱晃荡数值模拟方面,Shao等[10-11]对光滑粒子流体动力学法进行了改进,提高了数值精度,对横荡和横摇激励作用下的液舱晃荡进行了研究,并讨论了各种隔板类型的减晃效果.Zhang和Liu[12]提出了解耦有限粒子法,通过数值测试验证了该方法的准确性,并将其用于与二维液舱晃荡模拟.移动粒子半隐式法(moving particle semi-implicit,MPS)作为一种典型的粒子类方法也已广泛应用于液舱晃荡问题中,成为分析研究该问题不可或缺的技术手段.
Rueda等[13]应用MPS模拟了在波浪环境中,带流体液舱的运动响应,并通过傅里叶变换得到的幅值响应算子与实验比对吻合. 潘徐杰等[14]基于改进的MPS,比较了不同自由面条件、核函数对液舱晃荡数值模拟的影响.Lee等[15]用MPS方法模拟了在外流作用下带流体液舱的运动响应,并与无流体液舱的运动响应进行了对比,结果表明液舱内的流体能有效地减小液舱的运动响应.Tsukamoto等[16]在二维液舱中间布置了一个浮体,浮体与舱壁之间用弹簧连接,并用MPS方法研究了在不同充液率和激励频率下,流体对浮体的作用力.Zhang等[17]应用改进的MPS方法对二维液舱晃荡问题进行了数值模拟,并将计算结果与实验和网格类方法结果进行了对比,壁面砰击压力和自由面波形吻合较好.杨亚强[18]应用改进MPS方法对液舱晃荡进行了系统研究,包括激励频率和充液率对晃荡的影响、不同自由度激励下的晃荡特征、二维三维矩形或薄膜形液舱的晃荡,以及水平或垂直隔板对砰击压力和自由面破碎的抑制作用等.Zhang等[19-20]将MPS与有限元方法结合,研究了弹性液舱内的晃荡现象以及弹性隔板对晃荡的抑制效果.Wen等[21-22]开发了多相流MPS方法,并将该方法应用到双层和三层流体的晃荡问题中,计算波高和砰击压力与实验结果吻合较好.
虽然MPS方法可以对液舱晃荡问题进行有效地模拟,但其应用还大多数集中于二维问题.为实现MPS方法在三维液舱晃荡上的应用, 首先要解决的问题是提高计算效率.目前,常用的技术是多CPU并行计算,但是平衡每个CPU的计算负载具有一定的难度.图像处理器GPU最初被用来做图像运算工作,但由于其具有丰富的计算核心,十分适合大规模并行计算,目前已经广泛应用在人工智能、环境监测等领域. 近几年,将GPU并行加速技术应用到MPS方法中的研究也在逐步开展中.Hori等[23]开发了GPU加速的MPS方法程序,并对11万粒子的二维溃坝算例进行了模拟,加速比达到7倍. Zhu 等[24]通过对GPU不同内存使用的优化,大幅度提高了计算效率,对22万粒子的二维溃坝问题加速比达到26倍.Kakuda等[25-26]采用MPS方法在GPU设备上模拟了二维和三维溃坝问题,加速比分别为12倍和23倍.李海洲等[27]对MPS的邻居粒子搜寻和压力泊松方程进行了GPU加速,模拟了三维带障碍物溃坝和晃荡问题,每部分加速比均可达到10倍左右.Chen和Wan[28]在CUDA平台上开发了GPU加速的MPS方法求解器,并将其应用于模拟三维溃坝和液舱晃荡,加速比可以达到22倍.
本文将GPU加速技术与MPS方法相结合,开发了MPSGPU-SJTU求解器,对LNG型液舱晃荡进行了数值模拟.通过三种不同粒子间距 的数值计算验证了求解器的收敛性,其中最大的计算粒子个数达到200万.将GPU模拟结果与实验数据进行对比,并与CPU求解器对比计算效率,验证了MPSGPU-SJTU求解器的计算性能.本文还进一步研究了在不同充液率情况下LNG型液舱和方型液舱的不同晃荡现象,并对水和LNG两种不同介质的液舱晃荡特征进行了对比.
1 MPS数值方法
MPS方法是一种典型的基于拉格朗日描述流场的无网格粒子类方法,它最先由Koshizuka和Oka[29]在1996年提出,并用于模拟二维溃坝问题.该方法不需要离散N-S方程的对流项,可以有效地避免对流项离散而引起的数值发散问题,同时计算过程不需要使用网格,省去了网格生成与重构的繁杂过程,并且该方法易于追踪捕捉大变形或强非线性破碎的自由面.鉴于以上优点,越来越多的研究人员对MPS进行了深入研究,改进其数值模型提高计算精度,并将其应用于剧烈流动问题.在此,将简要介绍本文所采用的MPS方法的数值模型.1.1 控制方程
对于黏性不可压缩流体,MPS方法的控制方程包含连续方程和N-S方程$\nabla \cdot {\pmb V} = \dfrac{1}{\rho }\dfrac{{\rm D}\rho }{{\rm D}t} = 0 (1)$
$\dfrac{{\rm D}{\pmb V}}{{\rm D}t} = - \dfrac{1}{\rho }\nabla P + \nu \nabla ^2{\pmb V} + {\pmb g} (2)$
式中,${\pmb V}$为速度矢量, $\rho $ 为流体密度,$t$为时间,$P$为压力, $\upsilon $ 为运动黏性,${\pmb g}$为重力加速度矢量.
1.2 核函数
在MPS方法中,控制方程的微分项都是通过目标粒子与周围邻居粒子之间的相互作用来表征,核函数的主要作用是作为加权平均的权函数. 原始的核函数[29]如式(3)所示,当两个粒子距离很近时,核函数值会变得非常大,导致数值计算的不稳定. 因此,本文采用了一种无奇点的核函数[30],如式(4)所示$W\left( r \right) = \left\{ \!\!\begin{array}{ll} \dfrac{r_{\rm e} }{r} -1\,,& 0 \leqslant r < r_{\rm e} 0\,,& r_{\rm e} \leqslant r \end{array} \right. (3)$
$W\left( r \right) = \left\{ \begin{array}{ll} \dfrac{r_{\rm e} }{0.85r + 0.15r_{\rm e} } -1\,, & 0 \leqslant r < r_{\rm e} 0\,, & r_{\rm e} \leqslant r \end{array} \right. (4)$
式中,$r_{\rm e}$为粒子相互作用半径,$r$为两个邻居粒子的距离.其中,在粒子数密度模型和梯度模型中$r_{\rm e}=2.1 l_{0}$,在拉普拉斯模型中$r_{\rm e}=4.01 l_{0}$,$l_{0}$为初始粒子间距.
1.3 粒子作用模型
MPS方法中,控制方程中的微分算子都是基于粒子模型来进行离散的. 本文将介绍MPS方法中几个重要的粒子模型:梯度模型[31] (式(5))、散度模型[26] (式(6))和拉普拉斯模型[26] (式(7))$ \langle \nabla \phi \rangle_i = \dfrac{D}{n^0}\sum_{j \ne i} \dfrac{\phi _j + \phi _i }{ | {\pmb r}_j - {\pmb r}_i |^2} ( {\pmb r}_j - {\pmb r}_i ) \cdot W(| {\pmb r}_j - {\pmb r}_i | ) (5)$
$ \langle \nabla \cdot {\pmb V} \rangle_i = \dfrac{D}{n^0}\sum_{j \ne i} \dfrac{({\pmb V}_j - {\pmb V}_i ) \cdot ({\pmb r}_j - {\pmb r}_i )}{| {\pmb r}_j - {\pmb r}_i |^2} \cdot W(| {\pmb r}_j - {\pmb r}_i | ) (6)$
$ \langle \nabla ^2\phi \rangle_i = \dfrac{2D}{n^0\lambda }\sum_{j \ne i} (\phi _j - \phi _i ) \cdot W(| {\pmb r}_j - {\pmb r}_i | ) (7)$
$\lambda = \dfrac{\sum_{j \ne i} W(|{\pmb r}_j - {\pmb r}_i |) \cdot |{\pmb r}_j - {\pmb r}_i |^2} {\sum_{j \ne i} W(| {\pmb r}_j - {\pmb r}_i | )} (8)$
式中, $\phi $为任一物理量,$D$为空间维度,$n^{0}$为初始粒子数密度,${\pmb r}$为粒子坐标向量. 式(8)是一种守恒格式,其推导源于非定常扩散问题,是为了使数值结果与扩散方程的解析解相一致.
1.4 不可压缩模型
原始的压力泊松方程源项[26](式(9))完全基于粒子数密度[26](式(10)),而 粒子数密度场不光滑必然导致压力场的不光滑.Lee等[32]在2011年提出了一种结合速度散度和粒子数密度两个不可压缩条件的混合源项法,如式(11)$ \langle \nabla ^2P^{k + 1} \rangle_i = - \dfrac{\rho }{\Delta t^2}\dfrac{ \langle n^\ast \rangle _i - n^0}{n^0} (9)$
$ \langle n \rangle _i = \sum_{j \ne i} W\left( {\left| {\pmb r}_j - {\pmb r}_i \right|} \right) (10)$
$ \langle \nabla ^2P^{k + 1} \rangle _i = (1 - \gamma )\dfrac{\rho }{\Delta t}\nabla \cdot {\pmb V}_i^\ast - \gamma \dfrac{\rho }{\Delta t^2}\dfrac{ \langle n^\ast \rangle _i - n^0}{n^0} (11)$
式中,$\Delta t$为时间步长,${\pmb V}_i^\ast $为临时粒子速度矢量,$n^*$为临时粒子数密度,$\gamma $为常数取0.01.
1.5 自由面粒子判断
由于在MPS方法中,自由面粒子的压力被设为零作为压力边界条件,因此正确判断自由面粒子对数值模拟精度至关重要. 原始的MPS方法中,当粒子数密度满足$$ \langle n \rangle _i < \beta \cdot n^0 (12)$$
就被判断为自由面粒子, $\beta $为一常数.但是该判断方法精度不高,尤其当流动剧烈时,流体内部粒子常常会出现较小的粒 子数密度,容易造成误判.因此,Zhang和Wan[30]基于自由面粒子周围邻居粒子的不对称性分布如图1所示,提出了一种新的自由面粒子判断方法
${\pmb F}_i = \dfrac{D}{n^0}\sum_{j\ne i} \dfrac{1}{| {\pmb r}_i - {\pmb r}_j |} ({\pmb r}_i - {\pmb r}_j )W(r_{ij} ) (13)$
$\left| {\pmb F} \right| > 0.9\left| {\pmb F} \right|^0 (14)$
式中,$\left| {\pmb F} \right|^0$为$\left| {\pmb F} \right|$的初始值.当目标粒子满足式(14)则被判断为自由面粒子.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_1.jpg)
图1自由面粒子判断
-->Fig. 1Free surface detection
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1.6 边界条件
为了避免核函数在壁面处的截断,MPS方法采用布置多层粒子(一层壁面粒子,两层虚拟粒子)的方式保证壁面附近流场压力光滑和避免粒子穿透,如图2所示.壁面粒子的压力将和流体粒子一起参与压力泊松方程求解,虚拟粒子的压力将通过周围粒子插值得到.![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_2.jpg)
图2边界粒子示意图
-->Fig. 2Schematic of boundary particles
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1.7 计算流程
MPS方法采用半隐式方法求解流体的压力和速度. 每一个时间步迭代主要包含预测和修正两个部分. 第一步是根据重力和黏性力计算出流体的临时速度,如式(15)和式(16).第二步是由式(11)计算得到粒子的压力,根据压力场计算修正流体的速度和更新粒子的位置,如式(17)和 式(18)$\Delta {\pmb V}_i^\ast = \Delta t\left( {\nu \nabla ^2{\pmb V}_i^n + {\pmb g}} \right) (15)$
${\pmb V}_i^\ast = {\pmb V}_i^n + \Delta {\pmb V}_i^\ast (16)$
${\pmb V}_i^{n + 1} = {\pmb V}_i^\ast - \Delta t\dfrac{1}{\rho }\nabla P^{n + 1} (17)$
${\pmb r}_i^{n + 1} = {\pmb r}_i^n + \Delta t{\pmb V}_i^{n + 1} (18)$
2 GPU并行加速技术
从上述MPS方法介绍中,不难发现除了求解压力泊松方程,每个粒子的计算都是独立的. 研究人员在采用CPU并行加速技术时发现,增加CPU计算核心数可以有效地提高MPS方法的计算效率.相比CPU,GPU由于在相同芯片面积情况下划分了更多的算术逻辑单元ALU如图3所示,天然的众核硬件构架形式决定了GPU十分适合大规模并行科学计算.![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_3.jpg)
图3GPU和CPU的硬件架构
-->Fig. 3The hardware frameworks of GPU and CPU
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本文采用CUDA语言进行适用于CPU和GPU异构平台的求解器开发,它是由著名的半导体生产商NVIDIA公司推出的一种能以NVIDIA公司生产的GPU作为通用并行计算设备的开发平台.CUDA[33]使用C语言为基础,可以直接以大多数人熟悉的C语言,写出在显示芯片上执行的程序,而不需要去学习特定的显示芯片的指令或是特殊的结构. 在CUDA的架构下,一个程序分为两个部份:主机端和设备端.主机端是指在CPU上执行的部份,而设备端则是在GPU上执行的部份. 设备端的程序又称为kernel.通常主机端程序会将数据准备好后,复制到GPU显存中,再由GPU执行设备端程序,完成后再由主机端程序将结果从显存中取回.
如图4所示,在初始阶段,主机端程序将粒子数据和参数从CPU拷贝到GPU中. 此后,MPS方法的整个计算流程都由设备端程序实现在GPU上的高效并行运算.在整个计算流程中,所有的数据都保存在显存中,这样避免了在CPU和GPU之间数据传输的时间消耗.最终计算完成后,才将数据从GPU拷贝到CPU中进行保存. MPS方法在GPU端的程序计算主要包括以下8个步骤:
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_4.jpg)
图4MPS在GPU上运行的流程图
-->Fig. 4The flow chart of MPS on GPU
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(1)划分背景网格,搜寻邻居粒子,建立邻居粒子表.
(2)采用显式方法计算黏性力和重力.
(3)更新粒子的临时速度.
(4)计算粒子数密度.
(5)判断自由面粒子.
(6)构建压力泊松方程,采用隐式方法计算流场压力.
(7)插值得到第二类边界粒子压力,计算压力梯度.
(8)更新粒子速度和位置.
3 数值模拟
本文采用自主开发的求解器MPSGPU-SJTU在GPU设备上进行数值模拟. 为了验证GPU求解器的计算效率,本课题组开发的另一个在CPU设备上运行的求解器MLParticle-SJTU被用来作为对比. MLParticle-SJTU求解器已经应用于许多剧烈流动问题的模拟,如溃坝[34]、晃荡[18]、入水[35]、流固耦合[19]、波物作用[36],多相流[37]等.MPSGPU-SJTU和MLParticle-SJTU都是部署在高性能计算集群上运行. CPU为英 特尔E5-2680,主频2.8,GHz.GPU为英伟达P100,拥有3584个CUDA核心,16,GB显存. 两个求解器的数据格式均为双精度格式, 计算环境参数如表1所示.Table 1
表1
表1高性能计算集群参数
Table 1The computing environment of HPC cluster
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本文选取了蔡忠华[38]在2012年的三维LNG型液舱实验模型作为数值模型进行模拟. 图5展示了液舱的示意图,液舱长为0.834,m,宽为0.664,m,高为0.477,m,水深为0.334,m,充液率到达70%. 液舱将在转动激励作用下作纵摇简谐运动,运动方程如式(19)
$$\theta = \theta _0 \cdot \sin (\omega \cdot t) (19)$$
式中, $\theta _{0}$为液舱转动幅度,设为8$^\circ$,$\omega$为激励频率,设为0.85,Hz. 在液舱的侧面,布置了3个压力监测点,来监测侧壁面的砰击压力.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_6.jpg)
图5LNG型液舱模型示意图
-->Fig. 5Schematic of LNG tank
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3.1 粒子间距收敛性验证
本文首先对MPS方法的空间收敛性进行了验证. 选取了细(fine)中(middle)粗(coarse)三种不同的粒子分辨率,间距分别为4.5,mm, 6,mm和 7.5,mm,最大的粒子数达到了220万,时间步长统一取为0.5,ms,具体计算参数见表2.Table 2
表2
表2计算参数
Table 2Computational parameters
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图6展示了P2压力监测点处的压力变化曲线. 从图中可以看到,3种粒子间距的计算结果趋势基本一致. 表3统计了3种粒子间距从10,s到20,s内P2监测点的最大砰击压力平均值.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_8.jpg)
图6不同粒子间距在P2处的砰击压力
-->Fig. 6The impact pressure at P2 of different particle resolutions
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Table 3
表3
表3不同粒子间距在P2处的砰击压力
Table 3The impact pressure at P2 of different particle resolutions
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从表中可以看到,3种粒子间距的砰击压力差别不大,说明了求解器的收敛性良好.
本节选取了3种粒子间距数值模拟中间的1000个时间步,不包含保存数据,得到平均每一时间步的计算总时间(total),
压力泊松方程求解时间(PPE)和除压力泊松方程求解以外其他所有步骤的计算时间(others).
从图7和表4中可以看到,中粒子分辨率的单步计算时间大概是1.146 s,大概是粗粒子分辨率的2倍,细分辨率的1/3.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_10.jpg)
图7不同粒子间距的计算时间
-->Fig. 7The computation times of different particle resolutions
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Table 4
表4
表4不同粒子间距的计算时间
Table 4The computation times of different particle resolutions
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考虑计算精度和计算时间,本文后续数值模拟选取粒子间距为 6,mm.
3.2 数值结果验证
图8展示了一个周期内LNG型液舱晃荡的典型时刻流场图. 通过比较,GPU与CPU求解器模拟的流场基本一致.从图8(a)中观察到, 当液舱向左端倾斜时,流体也顺势向左端移动,此时自由液面呈现一定程度的内凹形状.随着液舱继续向左端倾斜,流体沿着液舱顶部斜边向上爬升,并拍击在顶部的两个拐角处,此时左端的自由液面和压力场都呈现出U字形.当液舱运动到最大幅值时,沿液舱顶部斜边爬升的两股流体在液舱顶部汇聚,并在顶部的正中心位置出现一个局部高压区.此时,流体沿着液舱顶部拐角向右流动形成两股射流,并伴有流体的飞溅.随后,液舱开始向右端倾斜,流体在惯性作用下依旧沿舱壁爬升,并沿着液舱的中纵剖面形成一股射流.随着液舱继续向右转动,流体也随之往右运动,从图8(a5)中可以看到,靠近前后舱壁的自由液面变得平坦,而液舱正中间的液面拱起明显高于其余部分的自由面,自由液面呈现出W字形. 随着液舱继续向右端倾斜,中间拱起的液面迅速平复,而靠近前后舱壁的自由液面迅速抬升,液面又重新呈现出U字形.最终,流体随着液舱的纵摇运动而表现出周期性的晃动.![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_12.jpg)
图8GPU和CPU模拟的液舱晃荡流场图
-->Fig. 8The flow fields of liquid sloshing by GPU and CPU simulations
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图9展示了P2点处各研究的砰击压力时历曲线. 图10展示了P2点处一个晃荡周期内的压力变化. MPSGPU-SJTU求解器计算的砰击压力曲线与其他模拟和实验结果能够较好地吻合,砰击压力的起始时刻和峰值基本一致.实验数据可以明显的看到有两个压力峰值,并在第一个压力峰值过来有明显的波动,但GPU数值模拟结果一个周期内存在连续3个压力峰值,并且后2个压力峰值大于实验结果,这可能是因为本文采用的MPS方法未采用多相流模型考虑气体卷入的影响.总体上,MPSGPU-SJTU求解器能够较准确地预测晃荡产生的壁面砰击压力.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_13.jpg)
图9不同研究在P2处的砰击压力
-->Fig. 9The impact pressure at P2 of different researches
-->
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_14.jpg)
图10P2处砰击压力的放大图
-->Fig. 10The enlarged signals of impact pressure at P2
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与上节相同,本节同样选取了数值模拟中间的1000个时间步进行对比.表5和图11显示了不同核数CPU和GPU的单步计算时间,压力泊松方程的求解依旧是MPS方法中最耗时的部分,占总体计算时间的90%.随着CPU的计算核心数的增加,计算时间会逐步减少.而对比GPU和CPU,无论是压力泊松方程求解还是其他部分计算,GPU的计算时间则大大地短于CPU.从图12中可以发现,其他部分的加速比远远大于压力泊松方程,但求解压力泊松方程的加速效果对MPS方法整体的计算效率起着决定性作用,如何采用GPU加速技术减少压力泊松方程计算时间依旧是需要解决的难点.在总计算时间上,GPU对单核CPU的加速比达到了106倍,对8核CPU的加速比达到了22倍,证明GPU并行加速是一种稳定可靠且适合于MPS方法的技术. 加速比$r_{\rm s}$可以通过式(20)计算得到
$$r_{\rm s} = \dfrac{t_{\rm CPU} }{t_{\rm GPU} } (20) $$
Table 5
表5
表5GPU和CPU的计算时间
Table 5The computation times of GPU and CPU
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![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_16.jpg)
图11GPU和CPU的计算时间
-->Fig. 11The computation times of GPU and CPU
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![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_17.jpg)
图12GPU加速比
-->Fig. 12The speedup ratio of GPU
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3.3 不同液舱构型晃荡对比
在以往的研究中,实验和数值模拟的液舱构型通常为方型,而实际液货船的液舱通常如图5所示为菱型. 因此,本节将在70%,50%和30% 三种不同充液率情况下,对方型液舱和LNG型液舱内的晃荡现象进行对比,分析两者不同.方型液舱模型如图13所示,液舱主尺度和测压点的布置均与LNG型液舱保持一致.主要计算参数和3.2节一样,粒子间距取6,mm,时间步长取 5,ms,3种不同充液率的纵摇幅度均取为8$^\circ$,激励频率分别为0.85,Hz (70%),0.75,Hz (50%),0.65,Hz (30%),接近于不同充液率下的一阶固有频率.![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_18.jpg)
图13方形液舱模型示意图
-->Fig. 13Schematic of rectangular tank
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3.3.1 70%充液率对比
图14展示了方型液舱的晃荡流场图. 液舱内流体同样随着液舱的纵摇运动而产生周期性的晃动. 如图14(a)所示,当液舱向左端倾斜时,自由液面上存在一个向左移动隆起的水头.水头的高度基本一致,自由液面并未像图8(a1)中出现U字形.当液舱继续向左端倾斜时,靠近液舱左端的水体堆积在一起,形成了台阶状.水体沿着舱壁向上爬升,整体拍击在了液舱顶部的拐角处,形成了带状的高压区,与LNG型液舱晃荡仅在一小块区域形成高压区不同.随后,流体沿着顶部舱壁向右流动形成了一平面射流,从图14(d)中可以清晰地看到流体的飞溅.最终,翻卷的自由液面在重力的作用下回落,又形成了一个隆起的水头,随着液舱向右端的转动而移动.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_19.jpg)
图14方型液舱晃荡流场图
-->Fig. 14The flow fields of liquid sloshing in rectangular tank
-->
图15和图16是不同液舱构型在连续几个周期和一个周期内的砰击压力时历曲线对比.对比二者结果,方型液舱3个压力监测点的 砰击压力峰值都明显大于LNG型液舱.当液舱转动到最大幅值时,流体拍击在液舱顶部的拐角,形成了P1点的瞬时峰值,P2和P3的最大砰击压力也出现在这个时刻.对于P1,方型液舱的平均最大压力值为3350,Pa,比LNG型液舱的平均最大压力值大了900,Pa. 对于P2,方型液舱的平均最大压力值为2600,Pa,LNG型液舱为1600,Pa.通过观察P2点处的砰击压力曲线发现,方型液舱的砰击压力在一个周期内出现了连续的两个峰值,而LNG型液舱则有3个峰值.P2处的第二个峰值是由于液舱开始向右端转动,拍击在液舱顶端的流体因为反作用力向下流动,而底部的流体因为惯性仍向上流动,二者的运动不同向造成了第二个峰值,如图8(a4)和图14(d)所示.LNG型液舱P2处的第三个峰值的存在是因为两边流体向中间挤压在中纵剖面处形成液面的拱起而造成的,如图8(a5)所示.对于P3压力检测点,两种构型的压力峰值差别 较小,静水压力为主要组成部分,拍击动压所占 比列较少.但是方型液舱由于自由液面整体起伏较大,在P3的压力曲线上出现几个小的压力峰值.而LNG型液舱自由液面相对平坦,P3处的压力基本仍旧表现为正弦变化.在充液率70%的情况下,LNG型的液舱构型设计更为合理,可以有效地减少液体晃荡对舱壁的砰击,更好地保护舱室结构.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_20.jpg)
图15不同液舱构型的砰击压力
-->Fig. 15The impact pressure in different tanks
-->
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_21.jpg)
图16砰击压力的放大图
-->Fig.16The enlarged signals of impact pressure
-->
3.3.2 50%充液率对比
图17展示了LNG型液舱的流场图,对比图8,50%充液率下LNG液舱内的自由液面变化更加剧烈.由于底部和顶部斜边的存在, LNG液舱晃荡呈现出非常强的三维特征.对比图8(a),图17(a)中自由液面的内凹形状更加明显,并且图17(e)中流体的飞溅现象更加显著. 但从图18中可以看到,方型液舱的自由液面整体十分的平整,流体晃荡运动幅度很小.图18(c)中仅有少量流体拍击到液舱顶部,随后自由面出现了小幅度的翻卷并落回整体流场.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_22.jpg)
图17LNG型液舱晃荡流场图
-->Fig. 17The flow fields of liquid sloshing in LNG tank
-->
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_23.jpg)
图18方型液舱晃荡流场图
-->Fig. 18The flow fields of liquid sloshing in rectangular tank
-->
图19和图20展示了50%充液率下LNG型液舱和方型液舱不同监测点的压力时历曲线. 从图中可以发现,LNG型液舱P1和P2处的最大砰击压力大于方型液舱,这是因为流体沿着液舱斜边爬升在顶部中央拍击形成一个局部高压区.P3点处两种液舱构型的压力基本相同,因为静水压力占据着主导成分.两种液舱构型在P2点处的压力曲线均表现出双峰值的现象,第一个峰值与P1点的峰值对应,是由流体拍击在液舱顶部造成, 第二个峰值是拍击流体回落到自由液面产生的.P3监测点处的压力也同样存在着双峰值,流体随着液舱的运动沿舱壁爬升形成了第一个压力峰值,自由液面的回落则产生第二个压力峰值. 对于3个压力监测点,方型液舱的最大压力峰值时间都早于LNG型液舱.这是因为方型液舱在晃荡过程中自由面平整,LNG型液舱的自由面则呈现凹字形向中间凸起的变化过程,而压力监测点布置在液舱的中纵剖面上,所以LNG型液舱的压力峰值呈现一定的滞后性.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_24.jpg)
图19不同液舱构型的砰击压力
-->Fig. 19The impact pressure in different tanks
-->
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_25.jpg)
图20砰击压力的放大图
-->Fig. 20The enlarged signals of impact pressure
-->
3.3.3 30%充液率对比
图21和图22展示了LNG型和方型液舱晃荡的流场图. LNG型液舱晃荡的自由面仍然存在着较强的三维特征. 在晃荡波传播过程中,自由面呈现凹型,仍在液舱顶部中间形成高压区,液体回落过程中呈现出W字形. 方型液舱在30%充液率的情况下,也呈现出了一定的三维特征. 从图22(c)中可以看到,方型液舱顶部存在着3个砰击区,并与图21(c)对比,方型液舱的中纵剖面处的流体连续性不如LNG型液舱. 当流体回落向另一个方向运动时,方向液舱的侧壁附近流体呈现出M字形.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_26.jpg)
图21LNG型液舱晃荡流场图
-->Fig. 21The flow fields of liquid sloshing in LNG tank
-->
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_27.jpg)
图22方型液舱晃荡流场图
-->Fig. 22The flow fields of liquid sloshing in rectangular tank
-->
图23展示了不同压力监测点的压力变化曲线,图24展示了一个周期内的压力变化放大图.从图中可以看到,两种液舱构型的压 力差别基本与50%充液率情况相同.对于P1和P2点,方型液舱的压力明显小于LNG型液舱,其中方型液舱在P2点处几乎没有压力,这是因为飞溅的流体与下部流体存在着间断. 由于液舱充液率较低,晃荡过程中流体的拍击飞溅等强非线性现象明显,自由液面变化复杂, 所以两种液舱构型P3点处的压力 在第一个峰值后均出现连续的波动.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_28.jpg)
图23不同液舱构型的砰击压力
-->Fig. 23The impact pressure in different tanks
-->
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_29.jpg)
图24砰击压力的放大图
-->Fig. 24The enlarged signals of impact pressure
-->
3.4 不同液体密度晃荡对比
由于条件的限制,实验难以再现真实的液化天然气在液舱中晃荡. 因此数值模拟成为一种方便可靠的技术手段. 本节模拟的液化天然气密度为450,kg/m$^{3}$,其他计算参数与表2相同,并与充水液舱晃荡结果进行对比,分析不同液体密度对液舱晃荡的影响.图25展示了液化天然气的晃荡流场图. 对比图8,虽然液舱内流体密度不同,但是不同密度流体的晃荡特征则基本相同. 液化天然气随着液舱摇动而周期性晃荡,并且自由液面同样呈现出U字形. 流体沿着液舱顶部斜边爬升,并在液舱顶部中间汇聚形成一个局部高压区. 当液舱向右端倾斜时,自由液面同样形成了中间高两边低的W字形状.
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_30.jpg)
图25液化天然气的液舱晃荡流场图
-->Fig. 25The flow fields of liquid sloshing of liquefied natural gas
-->
图26和图27展示了不同液体密度液舱晃荡在P2处的砰击压力时历曲线和一个周期内的压力变化.从图中可以发现不同介质的晃荡砰击压力的变化趋势基本完全一致,同样在一个周期内出现了3个压力峰值,无量纲后的砰击压力和砰击发生的时间几乎一样.在此,本文对3个压力监测点的最大砰击压力取平均值,量化对比不同液体密度的砰击压力,如表6所示.从表6的统计对比可以发现,砰击压力与流体密度之间基本满足正比关系.
$$\dfrac{pressure_{water} }{pressure_{LNG} } = \dfrac{density_{water} }{density_{LNG} } (21)$$
模拟结果表明,目前虽然无法对真实的液化天然气液舱晃荡开展实验研究,但是可以通过水介质的晃荡研究得出相应的 基本规律,并应用相似性换算得到液化天然气的晃荡结果,且具有一定的可靠性.
Table 6
表6
表6不同液体密度的砰击压力
Table 6The impact pressure of different fluid densities
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![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_32.jpg)
图26不同液体密度在P2处的砰击压力
-->Fig. 26The impact pressure at P2 of different fluid densities
-->
![](https://lxxb.cstam.org.cn/fileLXXB/journal/article/html/0459-1879-51-3-714/thumbnail/img_33.jpg)
图27P2处砰击压力的放大图
-->Fig. 27The enlarged signals of impact pressure at P2
-->
该结论与陆志妹等[39]的研究基本一致.
4 结论
本文通过将GPU加速技术引入MPS方法,开发了MPSGPU-SJTU求解器,对三维LNG型液舱晃荡进行数值模拟,计算最大粒子数超过200万个. 通过粒子间距收敛性验证以及GPU计算结果与和实验数据对比吻合,证明了MPSGPU-SJTU求解器的计算精度. 并通过与CPU求解器比较,证明了GPU加速技术可以大幅度地减少计算时间,GPUP100单卡对比CPU Intel E5-2680单核的加速比可以达到106倍.本文还研究了不同充液率下不同构型液舱内的晃荡现象,通过流场和砰击压力对比,证明了LNG型液舱在高充液率情况下具有较小的砰击压力,而在中低充液率情况下由于底部和顶部斜边的作用,晃荡流场存在着明显的三维特征,因此砰击压力反而大于方型液舱. 另一方面,本文进行了水和LNG两种介质的液舱晃荡计算和比较,总结出了水和LNG砰击压力的换算关系,证明了通过研究水介质晃荡而研究LNG晃荡的合理性. 但不同介质流体除了密度以外还存在其他参数的不同,今后需要对此问题开展更加深入的探讨,获得对不同介质晃荡关系的更准确认识.
The authors have declared that no competing interests exist.
参考文献 原文顺序
文献年度倒序
文中引用次数倒序
被引期刊影响因子
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[2] | . A nonlinear analysis is carried out for the motion of the inviscid, incompressible fluid, in a two-dimensional, rigid, open container which is subjected to forced sinusoidal pitching oscillation. Firstly, the problem is defined as a nonlinear initial-boundary value problem by the use of a governing differential equation and boundary conditions. Next, the problem is formulated in the form of a pseudo-variational principle, which provides a basis for the discretization. The finite element method and finite difference method are used spacewise and timewise, respectively. Due to the strong nonlinearity of the problem, an incremental method is used for the numerical analysis. Numerical results obtained by the present method are compared with solutions of the linear theory and experimental data. The difference between linear and nonlinear analysis has been clearly indicated |
[3] | . Deals with an application of the boundary element method to the analysis of nonlinear sloshing problems, namely nonlinear oscillations of a liquid in a container subjected to forced oscillations. First, the problem is formulated mathematically as a nonlinear initial-boundary value problem by the use of a governing differential equation and boundary conditions, assuming the fluid to be inviscid and incompressible and the flow to be irrotational. Next, the governing equation (Laplace equation) and boundary conditions, except the dynamic boundary condition on the free surface, are transformed into an integral equation by applying Green's formula. The dynamic boundary condition is reduced to a weighted residual equation by employing the Galerkin method. Numerical results obtained by the boundary element method are compared with those obtained by the conventional finite element method and also with existing analytical solutions of the nonlinear theory. Good agreement is obtained, and this indicates the availability of the boundary element method as a numerical technique for nonlinear free surface fluid problems |
[4] | . Sloshing flows in two- and three-dimensional prismatic tanks are considered in the present paper. A finite difference method is applied for simulating violent sloshing flows and impact occurrence. The computation focuses on the global flow and assumes a single-valued free-surface profile. For the simulation of impact occurrence near sloping boundaries, the concept of a buffer zone, previously used for impact simulation on the tank ceiling, is extended to sloping boundaries near the tank ceiling. For validation of the present numerical method, a comparison is made between the computational results for two-dimensional tanks and available experimental data, for which favorable agreement is shown. It is observed that the application of a buffer zone and a time-averaging scheme mitigates the sensitivity to grid resolution and time segment. Impact pressures on sloping boundaries and the tank ceiling for three-dimensional tanks are then compared with the results for two-dimensional tanks, which show higher peak pressures for the case of three-dimensional tanks. |
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[6] | . http://linkinghub.elsevier.com/retrieve/pii/S0045793011002921 |
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[8] | . 计算效率低的问题长期阻碍着无网格伽辽金法(element-free Galerkin method,EFGM)的深入发展.为了提高EFGM的计算速度,本文提出一种求解二维弹性力学问题的光滑无网格伽辽金法.该方法在问题域内采用滑动最小二乘法(moving least square,MLS)近似、在域边界上采用线性插值建立位移场函数;基于广义梯度光滑算子得到两层嵌套光滑三角形背景网格上的光滑应变,根据广义光滑伽辽金弱形式建立系统离散方程.两层嵌套光滑三角形网格是由三角形背景网格本身以及四个等面积三角形子网格组成.为了提高方法的精度,由Richardson外推法确定两层光滑网格上的最优光滑应变.几个数值算例验证了该方法的精度和计算效率.数值结果表明,随着光滑积分网格数目的增加,光滑无网格伽辽金法的计算精度逐步接近EFGM的,但计算效率要远远高于EFGM的.另外,光滑无网格伽辽金法的边界条件可以像有限元那样直接施加.从计算精度和效率综合考虑,光滑无网格伽辽金法比EFGM具有更好的数值表现,具有十分广阔的发展空间. . 计算效率低的问题长期阻碍着无网格伽辽金法(element-free Galerkin method,EFGM)的深入发展.为了提高EFGM的计算速度,本文提出一种求解二维弹性力学问题的光滑无网格伽辽金法.该方法在问题域内采用滑动最小二乘法(moving least square,MLS)近似、在域边界上采用线性插值建立位移场函数;基于广义梯度光滑算子得到两层嵌套光滑三角形背景网格上的光滑应变,根据广义光滑伽辽金弱形式建立系统离散方程.两层嵌套光滑三角形网格是由三角形背景网格本身以及四个等面积三角形子网格组成.为了提高方法的精度,由Richardson外推法确定两层光滑网格上的最优光滑应变.几个数值算例验证了该方法的精度和计算效率.数值结果表明,随着光滑积分网格数目的增加,光滑无网格伽辽金法的计算精度逐步接近EFGM的,但计算效率要远远高于EFGM的.另外,光滑无网格伽辽金法的边界条件可以像有限元那样直接施加.从计算精度和效率综合考虑,光滑无网格伽辽金法比EFGM具有更好的数值表现,具有十分广阔的发展空间. |
[9] | . 生物传热分析在低温外科手术、肿瘤热疗、病热诊断等临床医学治疗和诊断中有着广泛的应用. 由于健康皮肤组织内肿瘤的存在使得肿瘤附近区域的温度会明显升高, 这一特性常被用于检测皮肤组织内的肿瘤生长, 因此有必要开展生物传热数值分析的研究. 本文以含肿瘤的皮肤组织为研究对象, 将一种新型区域型无网格配点法——广义有限差分法应用于能描述含肿瘤皮肤组织传热过程的Pennes方程求解. 广义有限差分法利用泰勒展开式与移动最小二乘法将计算区域内的每个离散点上的物理量导数表示成其与邻近点物理量及权重系数的线性组合, 进而构建得到仅含各离散点未知物理量的线性方程组. 该方法不仅具有无需划分网格、避免数值积分等无网格配点法的优点, 同时还克服了大多数无网格配点法中插值矩阵高度病态的问题, 为此类方法在大规模工程数值计算中的应用提供了可能性. 本文首先介绍了模拟含肿瘤皮肤组织传热过程的广义有限差分法离散模型, 随后通过不含肿瘤与含规则形状肿瘤的基准算例, 检验广义有限差分法的计算精度与收敛性; 在此基础上, 通过数值模拟研究不同肿瘤形状及肿瘤位置分布对皮肤组织内温度分布的影响. . 生物传热分析在低温外科手术、肿瘤热疗、病热诊断等临床医学治疗和诊断中有着广泛的应用. 由于健康皮肤组织内肿瘤的存在使得肿瘤附近区域的温度会明显升高, 这一特性常被用于检测皮肤组织内的肿瘤生长, 因此有必要开展生物传热数值分析的研究. 本文以含肿瘤的皮肤组织为研究对象, 将一种新型区域型无网格配点法——广义有限差分法应用于能描述含肿瘤皮肤组织传热过程的Pennes方程求解. 广义有限差分法利用泰勒展开式与移动最小二乘法将计算区域内的每个离散点上的物理量导数表示成其与邻近点物理量及权重系数的线性组合, 进而构建得到仅含各离散点未知物理量的线性方程组. 该方法不仅具有无需划分网格、避免数值积分等无网格配点法的优点, 同时还克服了大多数无网格配点法中插值矩阵高度病态的问题, 为此类方法在大规模工程数值计算中的应用提供了可能性. 本文首先介绍了模拟含肿瘤皮肤组织传热过程的广义有限差分法离散模型, 随后通过不含肿瘤与含规则形状肿瘤的基准算例, 检验广义有限差分法的计算精度与收敛性; 在此基础上, 通过数值模拟研究不同肿瘤形状及肿瘤位置分布对皮肤组织内温度分布的影响. |
[10] | . Smoothed particle hydrodynamics (SPH) is a popular meshfree, Lagrangian particle method with attractive features in modeling liquid sloshing dynamics, which is usually associated with changing and breakup of free surfaces, strong turbulence and vortex, and “violent” fluid–solid interaction. This paper presents an improved SPH method for modeling liquid sloshing dynamics. Firstly, modified schemes for approximating density (density correction) and kernel gradient (kernel gradient correction, or KGC) have been used to achieve better accuracy with smoother pressure field. Secondly, the Reynolds Averaged turbulence model is incorporated into the SPH method to describe the turbulence effects. Thirdly, a coupled dynamic solid boundary treatment (SBT) algorithm has been proposed to improve the accuracy near the solid boundary areas. The new SBT algorithm consists of a kernel-like, soft repulsive force between approaching fluid and solid particles, and a reliable numerical approximation scheme for estimating field functions of virtual solid particles. Three numerical examples are modeled using this improved SPH method, and the obtained numerical results agree well with experimental observations and results from other sources. |
[11] | . Abstract Purpose - The purpose of this paper is to investigate different baffles on mitigating liquid sloshing in a rectangular tank due to a horizontal excitation and to find out the optimal selection of sloshing mitigation for practical applications. Design/methodology/approach - The numerical study is conducted by using a proven improved smoothed particle hydrodynamics (SPH), which is convenient in tracking free surfaces and capable of obtaining smooth and correct pressure field. Findings - Liquid sloshing effects in a rectangular tank with vertical middle baffles, horizontal baffles, T-shape baffles and porous baffles are investigated together with those without any baffles. It is found that the existence of baffles can mitigate sloshing effects and the mitigation performance depends on the shape, structure and location of the baffles. Considering the balance of sloshing mitigation performance and the complexity in structure and design, the I shaped and T shaped baffles can be good choices to mitigate sloshing effects. Practical implications - The presented methodology and findings can be helpful in practical engineering applications, especially in ocean engineering and problems with large sloshing effects. Originality/value - The SPH method is a meshfree, Lagrangian particle method, and therefore it is an attractive approach for modeling liquid sloshing with material interfaces, free surfaces and moving boundaries. In most previous literature, only simple baffles are investigated. In this paper, more complicated baffles are investigated, which can be helpful in practical applications and engineering designs. |
[12] | . Smoothed particle hydrodynamics (SPH) is a meshfree Lagrangian particle method, and it has been applied to different areas in engineering and sciences. One concern of the conventional SPH is its low accuracy due to particle inconsistency, which hinders the further methodology development. The finite particle method (FPM) restores the particle consistency in the conventional SPH and thus significantly improves the computational accuracy. However, as pointwise corrective matrix inversion is necessary, FPM may encounter instability problems for highly disordered particle distribution. In this paper, through Taylor series analyses with integration approximation and assuming diagonal dominance of the resultant corrective matrix, a new meshfree particle approximation method, decoupled FPM (DFPM), is developed. DFPM is a corrective SPH method, and is flexible, cost-effective and easy in coding with better computational accuracy. It is very attractive for modeling problems with extremely disordered particle distribution as no matrix inversion is required. One- and two- dimensional numerical tests with different kernel functions, smoothing lengths and particle distributions are conducted. It is demonstrated that DFPM has much better accuracy than conventional SPH, while particle distribution and the selection of smoothing function and smoothing length have little influence on DFPM simulation results. DFPM is further applied to model incompressible flows including Poiseuille flow, Couette flow, shear cavity and liquid sloshing. It is shown that DFPM is as accurate as FPM while as flexible as SPH, and it is very attractive in modeling incompressible flows with possible free surfaces. |
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[14] | . 使用移动粒子半隐式法(MPS)模拟了液舱晃荡现象。模拟中选用了3种不同的典型核函数,结果表明,有限值的核函数更适合晃荡现象的模拟。针对由自由表面判定条件引起的压力震荡现象,本文使用了不同的自由表面判定条件,发现较小β能够减少由自由表面判定条件引起的压力震荡;进而使用面积-时间平均法处理压力震荡,取得了不错的效果。在面积平均法中,使用了一种权重式平均法,以减轻平均面积中存在压力畸点的影响;在时间平均法中,结果表明在合适的范围内,平均时间段越长,消除压力震荡的效果就越明显。 . 使用移动粒子半隐式法(MPS)模拟了液舱晃荡现象。模拟中选用了3种不同的典型核函数,结果表明,有限值的核函数更适合晃荡现象的模拟。针对由自由表面判定条件引起的压力震荡现象,本文使用了不同的自由表面判定条件,发现较小β能够减少由自由表面判定条件引起的压力震荡;进而使用面积-时间平均法处理压力震荡,取得了不错的效果。在面积平均法中,使用了一种权重式平均法,以减轻平均面积中存在压力畸点的影响;在时间平均法中,结果表明在合适的范围内,平均时间段越长,消除压力震荡的效果就越明显。 |
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[16] | . In order to investigate the effects of an elastically-linked moving body on liquid sloshing inside a tank, an analytical formulation and a numerical approach were proposed to assess hydrodynamic loads in a partially filled rectangular tank with a body connected to the tank by springs. The analytical approach was developed based on the potential theory to calculate fluid velocity field, and the dynamics of the liquid sloshing coupled to the moving body are described as a mechanical system with two degrees of freedom. The coupling between the fluid and the moving body is given by a damping force calculated based on the body geometry and the fluid velocity field. The proposed numerical approach is based on the Moving Particle Semi-implicit (MPS) method, which is a Lagrangian particle-based method and very effective to model nonlinear hydrodynamics due to fluid鈥搒tructure interaction. In the numerical approach, the rigid body is modeled as a cluster of particles and the motions are calculated considering its mass, moment of inertia, hydrodynamic loads and springs restoring forces. The elastic link between the body and tank is modeled by applying Hooke鈥檚 law. Simple cases of floating body motion were used to validate the numerical method. Finally, analytical and numerical results were compared. Despite its simplicity, the analytical approach proposed in the present work is an efficient approach to provide qualitative understanding and a first estimate of the moving body effects on the sloshing inside the tank. On the other hand, the numerical approach can provide more detailed information about the coupling phenomena, and it is an effective mean for the assessment of the reduction of the sloshing loads due to the moving body with elastic link. Finally, the effectiveness of the concept as a sloshing suppressing device is also investigated. |
[17] | . This paper presents a comparative study of a meshless moving particle semi-implicit (MPS) method and a grid based level-set method in the simulation of sloshing flows. The numerical schemes of the MPS and level-set methods are outlined and two violent sloshing cases are considered. The computed results are compared with the corresponding experimental data for validation. The impact pressure and the deformations of free surface induced by sloshing are comparatively analyzed, and are in good agreement with experimental ones. Results show that both the MPS and level-set methods are good tools for simulation of violent sloshing flows. However, the second pressure peaks as well as breaking and splashing of free surface by the MPS method are captured better than by the level-set method. |
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[19] | . As more and more liquid carriers with huge size are manufactured to support the transportation demand of natural resources, risks such as local deformation or even damage of cargo containment systems resulting from sloshing phenomenon subsequently increase, and it's necessary to take the elasticity of tank walls into account in the researches of sloshing phenomenon. In present paper, we numerically studied the interaction between liquid sloshing flow and elastic bulkheads of liquid carrier by fully Lagrangian particle method, MLParticle-SJTU solver, which is an in-house solver developed based on the moving particle semi-implicit (MPS) method. Coupled with the finite element method (FEM), the MLParticle-SJTU solver is extended to numerical analysis of elastic structural response due to the impact loads of sloshing flows. To validate the feasibility of the MPS-FEM coupled solver in dealing with fluid structure interaction (FSI) problems, a benchmark of dam-breaking flow interacting with elastic lateral wall is studied firstly and results show good agreement with published data. Then, the sloshing phenomenon in an elastic tank is numerically investigated. By varying the Young's modulus of tank walls, interesting characteristics regarding evolutions of free surface, variation of impact pressures, dynamic responses of the structures in both time and frequency domains are presented. |
[20] | . Fluid-structure interaction(FSI)problems caused by fluid impact loads are commonly existent in naval architectures and ocean engineering fields. For instance,the impact loads due to non-linear fluid motion in a liquid sloshing tank potentially affect the structural safety of cargo tanks or vessels. The challenges of numerical study on FSI problems involve not only multidisciplinary features,but also accurate description of non-linear free surface. A fully Lagrangian particle-based method,the moving particle semi-implicit and finite element coupled method(MPS-FEM),is developed to numerically study the FSI problems. Taking into account the advantage of the Lagrangian method for large deformations of both fluid and solid boundaries,the MPS method is used to simulate the fluid field while the finite element method(FEM)to calculate the structure field. Besides,the partitioning strategy is employed to couple the MPS and FEM modules. To validate accuracy of the proposed algorithm,a benchmark case is numerically investigated. Both the patterns of free surface and the deflections of the elastic structures are in good agreement with the experimental data. Then,the present FSI solver is applied to the comparative study of the mitigating effects of rigid baffles and elastic baffles on the sloshing motions and impact loads. |
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[23] | . The MPS (Moving Particle Semi-implicit) method has been proven useful in computation free-surface hydrodynamic flows. Despite its applicability, one of its drawbacks in practical application is the high computational load. On the other hand, Graphics Processing Unit (GPU), which was originally developed for acceleration of computer graphics, now provides unprecedented capability for scientific computations. The main objective of this study is to develop a GPU-accelerated MPS code using CUDA (Compute Unified Device Architecture) language. Several techniques have been shown to optimize calculations in CUDA. In order to promote the acceleration by GPU, particular attentions are given to both the search of neighboring particles and the iterative solution of simultaneous linear equations in the Poisson Pressure Equation. In this paper, 2-dimensional calculations of elliptical drop evolution and dam break flow have been carried out by the GPU-accelerated MPS method, and the accuracy and performance of GPU-based code are investigated by comparing the results with those by CPU. It is shown that results of GPU-based calculations can be obtained much faster with the same reliability as the CPU-based ones. |
[24] | The Moving Particle Semi-implicit (MPS) method performs well in simulating violent free surface flow and hence becomes popular in the area of fluid flow simulation. However, the implementations of searching neighbouring particles and solving the large sparse matrix equations (Poisson-type equation) are very time-consuming. In order to utilize the tremendous power of parallel computation of Graphics Processing Units (GPU), this study has developed a GPU-based MPS model employing the Compute Unified Device Architecture (CUDA) on NVIDIA GTX 280. The efficient neighbourhood particle searching is done through an indirect method and the Poisson-type pressure equation is solved by the Bi-Conjugate Gradient (BiCG) method. Four different optimization levels for the present general parallel GPU-based MPS model are demonstrated. In addition, the elaborate optimization of GPU code is also discussed. A benchmark problem of dam-breaking flow is simulated using both codes of the present GPU-based MPS and the original CPU-based MPS. The comparisons between them show that the GPU-based MPS model outperforms 26 times the traditional CPU model. |
[25] | . Abstract An acceleration of the particle-based incompressible fluid flow simulations on GPU using CUDA is presented. The particle method is based on the MPS (Moving Particle Semi-implicit) scheme using logarithmic-type weighting function to stabilize the spurious oscillatory solutions for the pressure fields which are governed by Poisson equation. The standard MPS scheme is widely utilized as a particle strategy for the free surface flow, the problem of moving boundary, multi-physics/multi-scale ones, and so forth. Numerical results demonstrate the workability and the validity of the present approach through dam-breaking flow problem. |
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[27] | . MPS(Moving Particle Semiimplicit)法能够有效地处理溃坝、晃荡等自由面大变形流动问题。在三维MPS方法中,粒子数量的急剧增加会导致其计算效率的降低并限制其在大规模流动问题中的应用。基于自主开发的MPS求解器MLParticle-SJTU,本文对求解过程中耗时最多的邻居粒子搜寻和泊松方程求解两个模块采用了GPU并行加速,详细探讨了CPU GPU策略。以三维晃荡和三维溃坝这两种典型的自由面大变形流动为例,比较了CPU GPU相对于MLParticleSJTU串行求解时的加速情况,结果表明CPU GPU在邻居粒子和泊松方程这两个模块中的加速比最高能达到十倍左右。此外,采用CPU GPU并行能够较准确地模拟溃坝、晃荡等自由面大变形问题。 . MPS(Moving Particle Semiimplicit)法能够有效地处理溃坝、晃荡等自由面大变形流动问题。在三维MPS方法中,粒子数量的急剧增加会导致其计算效率的降低并限制其在大规模流动问题中的应用。基于自主开发的MPS求解器MLParticle-SJTU,本文对求解过程中耗时最多的邻居粒子搜寻和泊松方程求解两个模块采用了GPU并行加速,详细探讨了CPU GPU策略。以三维晃荡和三维溃坝这两种典型的自由面大变形流动为例,比较了CPU GPU相对于MLParticleSJTU串行求解时的加速情况,结果表明CPU GPU在邻居粒子和泊松方程这两个模块中的加速比最高能达到十倍左右。此外,采用CPU GPU并行能够较准确地模拟溃坝、晃荡等自由面大变形问题。 |
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[29] | . A moving-particle semi-implicit (MPS) method for simulating fragmentation of incompressible fluids is presented. The motion of each particle is calculated through interactions with neighboring particles covered with the kernel function. Deterministic particle interaction models representing gradient, Laplacian, and free surfaces are proposed. Fluid density is implicitly required to be constant as the incompressibility condition, while the other terms are explicitly calculated. The Poisson equation of pressure is solved by the incomplete Cholesky conjugate gradient method. Collapse of a water column is calculated using MPS. The effect of parameters in the models is investigated in test calculations. Good agreement with an experiment is obtained even if fragmentation and coalescence of the fluid take place. |
[30] | . Liquid sloshing is a kind of nonlinear free-surface flows.In low-filling tank,sloshing shows strong nonlinearity due to the large space for liquid motion.The free surface will happen to be deformed greatly,merged and broken.Simulation of such complicated flows is a challenging task.In this paper,the liquid sloshing in low-filling tank is simulated based on Moving Particle Semi-Implicit(MPS) method.Results show that the liquid impacts the ceiling of the tank,and splashes,when the oscillation frequency is equal to the natural frequency.A large impact pressure on the side wall is observed.At a lower oscillation frequency,the wave in the tank is broken,and turns over.A lower impact pressure on the side wall is measured.Numerical results illustrate that the MPS method can predict the impact behavior induced by liquid sloshing.The calculated pressure is in good agreement with experimental data.The presented MPS method is proved to have good flexibility in dealing with the complex free surface flows with broken and merged waves. |
[31] | . In this paper, a method to stabilize simulations and suppress the pressure oscillation in Moving Particle Semi-implicit method for an incompressible fluid is presented. To make the pressure smooth in terms of both of space and time, a new representation of the incompressible condition is proposed. The incompressible condition consists of two parts: the Divergence-Free condition and the Particle Number Density condition. The Divergence-Free condition has the effect of making the pressure smooth in terms of both space and time. The Particle Number Density condition is necessary to keep the fluid volume constant. In this work, the Quasi-Compressibility is also introduced for stabilization. A dam break is simulated more stably and the space distribution and the time variation of pressure are evaluated more smoothly than the traditional method. Moreover, surface particles are detected more accurately. Nevertheless the proposed method is computationally cheaper. Some simulations such as a Fluid鈥揝tructure Interaction are supposed to be more accurate using this method. |
[32] | . The violent free-surface motions and the corresponding impact loads are numerically simulated by using the Moving Particle Semi-implicit (MPS) method, which was originally proposed by Koshizuka and Oka [10] for incompressible flows. In the original MPS method, there were several defects including non-optimal source term, gradient and collision models, and search of free-surface particles, which led to less-accurate fluid motions and non-physical pressure fluctuations. In the present study, how those defects can be remedied is illustrated by step-by-step improvements in the respective processes of the revised MPS method. For illustration, two examples are studied; (i) dam breaking problem and (ii) liquid sloshing inside a rectangular tank. The improvement of each step is explained and numerically demonstrated. The numerical results are also compared against the experimental results of Martin and Moyce [12] for dam-breaking problem and Kishev et al. [9] for sloshing problem. The numerical results for violent free-surface motions and impact pressures are in good agreement with their experimental data. |
[33] | |
[34] | . MPS(Moving Particle Semi-Implicit)方法是一种拉格朗日粒子法,在处理大变形流动问题中具有很大的优势.将MPS方法应用到三维溃坝流动问题中,并对粒子的移动方式进行了修改,改进后的方法(XMPS)可以使粒子移动更加有序,避免粒子间的相互穿透.数值计算结果表明:MPS方法(包括XMPS)在处理复杂的自由面流动问题中具有很好的灵活性和可靠性,数值模拟能够比较准确地预测出自由面的形状和位置,即使在水面出现翻卷、入水和水柱撞击到障碍物时,数值结果仍然能够与实验相吻合.从细节上看,XMPS可以给出更为清晰、光滑的自由面形状,并能更好地捕捉到流动的细节特征. MPS(Moving Particle Semi-Implicit)方法是一种拉格朗日粒子法,在处理大变形流动问题中具有很大的优势.将MPS方法应用到三维溃坝流动问题中,并对粒子的移动方式进行了修改,改进后的方法(XMPS)可以使粒子移动更加有序,避免粒子间的相互穿透.数值计算结果表明:MPS方法(包括XMPS)在处理复杂的自由面流动问题中具有很好的灵活性和可靠性,数值模拟能够比较准确地预测出自由面的形状和位置,即使在水面出现翻卷、入水和水柱撞击到障碍物时,数值结果仍然能够与实验相吻合.从细节上看,XMPS可以给出更为清晰、光滑的自由面形状,并能更好地捕捉到流动的细节特征. |
[35] | . 3D violent free-surface flows are modelled by multi-resolution moving particle semi-implicit (MPS) method. Firstly, a 2D dam-break flow with an obstacle is performed. This shows that multi-resolution... |
[36] | . Slamming is the phenomenon of structure impacting the water surface. It always results in the extremely high load on the structure. This paper is mainly concerned with the slamming force caused by the wave-plate interaction. In this paper, the process of solitary wave impacting onto the horizontal plate is simulated with the help of the moving particle semi-implicit and finite element coupled method(MPS-FEM). The MPS method is adopted to calculate the fluid domain while the structural domain is solved by FEM method. In the first series of simulations, the profiles of the solitary waves with various amplitudes, which are generated in the numerical wave tank, are compared with the theoretical results. Thereafter the interaction between the solitary waves and a rigid plate is simulated. The effects of wave amplitude, as well as the elevation of the plate above the initial water level, on the slamming force are numerically investigated. The calculated results are compared with the available experimental data. Finally, the interactions between the solitary waves and the elastic plate are also simulated. The effects of the structural flexibility on the wave-induced force are analyzed by the comparison between the cases with elastic and the rigid plate. |
[37] | . The Rayleigh鈥揟aylor instability (RTI) problem is one of the classic hydrodynamic instability cases in natural scenarios and industrial applications. For the numerical simulation of the RTI problem, this paper presents a multiphase method based on the moving particle semi-implicit (MPS) method. Herein, the incompressibility of the fluids is satisfied by solving a Poisson Pressure Equation (PPE) and the pressure fluctuation is suppressed. A single set of equations is utilized for fluids with different densities, making the method relatively simple. To deal with the mathematical discontinuity of density in the two-phase interface, a transitional region is introduced into this method. For particles in the transitional region, a density smoothing scheme is applied to improve the numerical stability. The simulation results show that the present MPS multiphase method is capable of capturing the evolutionary features of the RTI, even in the later stage when the two-phase interface is quite distorted. The unphysic... |
[38] | . . |
[39] | // 液舱晃荡是LNG船不可避免的问题,其产生的冲击载荷有可能造成LNG船液舱内壁结构的疲劳和破坏,进而导致易燃液体的泄漏、火灾甚至爆炸。准确预报液舱晃荡产生的冲击载荷至关重要。由于LNG易燃易爆,液舱晃荡模型试验通常采用水介质模拟液舱晃荡,由于密度和黏性的不同,液体晃荡自由面的形态存在差异,载荷预报的精度难以保证。基于Fluent软件平台,进行水和LNG两种介质液舱晃荡的系列计算,并与试验进行比较。为简化计算,假定液舱模型作正弦简谐运动,其幅值相应于实船运动的十一平均幅值,周期相应于平均过零周期。针对某LNG的液舱,比较分析LNG和水两种介质液舱晃荡的冲击载荷,提出由水介质晃荡载荷模型试验结果换算至LNG介质的方法。 // 液舱晃荡是LNG船不可避免的问题,其产生的冲击载荷有可能造成LNG船液舱内壁结构的疲劳和破坏,进而导致易燃液体的泄漏、火灾甚至爆炸。准确预报液舱晃荡产生的冲击载荷至关重要。由于LNG易燃易爆,液舱晃荡模型试验通常采用水介质模拟液舱晃荡,由于密度和黏性的不同,液体晃荡自由面的形态存在差异,载荷预报的精度难以保证。基于Fluent软件平台,进行水和LNG两种介质液舱晃荡的系列计算,并与试验进行比较。为简化计算,假定液舱模型作正弦简谐运动,其幅值相应于实船运动的十一平均幅值,周期相应于平均过零周期。针对某LNG的液舱,比较分析LNG和水两种介质液舱晃荡的冲击载荷,提出由水介质晃荡载荷模型试验结果换算至LNG介质的方法。 |