Dynamic response of flowing ice colliding with a sluice pier under hydrodynamic action
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摘要: 高寒地区河冰撞击河道的闸墩结构会产生极端冰载荷和冰激振动,水的动力效应使得碰撞过程更加复杂。采用任意拉格朗日-欧拉流固耦合方法,考虑作用在流冰和闸墩表面的流体力,建立了水-冰-闸墩耦合模型,探究了偶然极端条件下冰-闸墩碰撞的力学特性,设计了冰-砼碰撞实验。结果表明:冰-砼碰撞实验中,撞击力的模拟结果与实验结果吻合良好;对流固耦合的水动力效应分析发现,水-冰-闸墩耦合模型能够体现水的流体特性,在流冰撞击闸墩近场逼近过程中,初始时刻水的动力效应能够增加流冰的动能,撞击楔入闸墩过程中,水介质形成一个瞬态高压力场,产生水垫效应吸收冰体部分动能,从而抑制流冰运动;在不同流冰体积和压缩强度工况下,闸墩结构所承受的冰力随着流冰体积的增大而增大,流冰压缩强度对冰力的影响较小,流冰损伤与闸墩结构响应主要集中在碰撞接触区,流冰撞击闸墩结构引起冰激振动,流冰体积对闸墩振动加速度的影响较大,相同体积的流冰随着压缩强度的增大,振动幅值差异不明显,表明流冰体积是影响冰-闸墩碰撞的关键参数。Abstract: In frigid regions, the construction of sluice pier structures within river systems is confronted with considerable challenges arising from the presence of severe ice loads and ice-induced vibrations. The collision process between ice and sluice piers is further complicated due to the intricate hydrodynamic effects exerted by water. The arbitrary Lagrangian-Eulerian (ALE) fluid-structure interaction (FSI) method is employed in this research to meticulously account for the fluid forces acting upon both the ice and sluice pier surfaces. A comprehensive coupled model encompassing the interactions among water, ice, and sluice piers is established to thoroughly investigate the mechanical characteristics associated with ice-sluice pier collisions under highly unpredictable conditions. Corresponding ice-concrete collision tests are meticulously designed and conducted, revealing an exemplary concurrence between the simulated impact forces and the values obtained from experimental observations. Upon analyzing the fluid-structure interaction and hydrodynamic effects, the present study demonstrates that the water-ice-sluice pier coupled model adeptly captures the fluid characteristics inherent to water. During the approach of an ice mass towards a sluice pier, the initial hydrodynamic effects initiated by the water medium effectively augment the kinetic energy possessed by the ice. As the ice forcefully interacts with the sluice pier, the water medium swiftly generates a transient high-pressure field, thereby establishing a phenomenon colloquially referred to as the water cushion effect. This effect is manifested by absorbing a portion of the ice’s kinetic energy, effectively dampening its movement. Distinctive scenarios characterized by varying ice volumes and compression strengths elucidate that the ice forces exerted upon the sluice pier structure directly correlate with the magnitude of the ice volume, while the influence of ice compression strength on said forces is relatively negligible. The consequential damages inflicted upon the ice and the response exhibited by the sluice pier structure primarily manifest within the contact area at the moment of collision. Consequently, the collisions between ice and the sluice pier structure induce vibrations that are uniquely attributed to ice-related factors. The volume of ice significantly influences the acceleration of sluice pier vibrations. Furthermore, under the condition of maintaining a consistent ice volumes, an increase in compression strength yields only marginal discrepancies in vibration amplitude. This finding convincingly substantiates the critical role played by ice volume as the paramount parameter governing ice-sluice pier collisions.
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Key words:
- fluid-structure interaction /
- hydrodynamic /
- sluice pier /
- collision forces /
- ice-induced vibration
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随着脉冲功率技术和高功率激光技术的发展,采用脉冲大电流和高功率脉冲激光对物质进行无冲击斜波压缩的实验技术在过去的十余年中获得了长足的进步[1-5],并成功应用于极端条件下(高压、高应变率)的状态方程[6-10]、高压强度[11-15]、相变[16-18]等材料物性的研究。在斜波压缩实验中,可测量的物理量主要是台阶靶不同Lagrange位置的样品界面粒子速度,如何通过界面粒子速度获取实验材料的动力学响应,成了此类实验必须解决的问题。
针对斜波压缩实验数据为台阶靶样品自由面或样品/窗口界面速度历史的情形,多种方法(Lagrange方法[19]、反积分方法[20-21]和特征线方法[22-23])被提出用于获取材料的压力-比容关系。反积分方法和特征线方法都是先假定材料参数,以实验测量的界面速度作为输入在时间轴逆向求解,其中反积分还要以不同厚度样品的加载面加载历史一致作为收敛的单一判据,因此对考虑诸如强度等力学特性的材料,需要预先设定的模型参数越多,该方法的使用难度就越大;此外,反积分方法和特征线方法要求材料模型参数的初设值与其真实值的偏差不能太大,否则会出现计算不收敛或收敛参数无意义的情况。采用Lagrange方法的优点是不需对材料参数做任何假定,可用于处理材料的复杂力学响应,但难点在于如何获得准确的原位粒子速度剖面。早期的工作采用自由面速度近似法[19]计算原位速度;后来Volgler等人发展了增量阻抗匹配法[24];2013年,J.L.Brown等提出了转换函数法(transfer function method,TFM)[25]。数值计算表明,采用转换函数方法可准确获得斜波压缩实验中的加载-卸载原位速度剖面,但前提是使用该方法过程中数值模拟的界面速度曲线和实验测量的速度曲线尽可能的一致。
为避免J.L.Brown等提出的使用转换函数方法中需进行高精度磁流体数值计算的需求,本文中提出一种联合使用正向Lagrange方法和转换函数来处理斜波压缩实验数据的新途径,分析转换函数方法的使用条件,并在此基础上讨论转换函数方法在斜波压缩下强度实验数据处理中的应用。
1. Lagrange正向数据处理方法
在Lagrange坐标下,一维等熵运动中的质量、动量和能量守恒方程可表达为[19]:
{l2/∂σ/∂h=−ρ0∂u/∂t(l1∂u/∂h=−∂ε/∂t(σ/ρ0)(∂u/∂h)=−∂e/∂t (1) 式中:σ为应力(压力为正号),ε为应变,ρ0为初始密度,u为粒子速度,e为比内能,h、t为Lagrange坐标和时间,Lagrange声速的定义CL=Δh/Δt,上式给出等熵线上扰动形成的状态增量形式为:
{l2/Δσ=−ρ0CL(u)Δu(l1Δu=−CL(u)ΔεΔe=σΔε/ρ0 (2) 由此可计算材料的应力-应变关系为:
Δσ=ρ0C2LΔε (3) 采用Lagrange方法处理斜波压缩实验数据时,基本处理流程见图 1。在同一发实验中,测量不同厚度样品的自由面或样品/窗口界面粒子速度,将实验测量的界面速度转换为原位速度(in-situ velocity)后,再对不同厚度样品的速度-时间曲线做差,进而得出Lagrange波速与粒子速度关系。通过式(2),可计算给出整个加载-卸载过程的CL-u、σ-u、σ-ε曲线。显而易见,Lagrange正向数据处理的难点在于如何准确还原不同厚度样品的原位粒子速度。
2. 转换函数方法
转换函数方法(TFM)的物理思想为:假定数值计算可以准确的表征样品后界面反射波与前界面后续加载波的相互作用,采用数值计算给出后界面速度和原位速度之间的映射关系,将该映射关系对实验测量的速度剖面进行反演,即可获得实验对应的原位速度。该方法自2013年提出以来,在Sandia实验室迅速获得广泛应用[8, 14, 25-26]。和自由面近似以及增量阻抗匹配方法相比,转换函数方法中可以考虑界面反射波与后续加载波的相互作用,准确的将非简单波情形还原为简单波情形。
转换函数方法的使用步骤可归纳如下。
(1) 采用数值计算,获得样品/窗口界面的粒子速度剖面uwc(t)和相同位置的原位速度剖面uic(t),要求计算的uwc(t)尽可能的和实验测量的样品/窗口界面速度剖面uwe(t)接近。
(2) 寻找uwc(t)和uic(t)之间的转换函数f(t)。先将uwc(t)和uic(t)变换到频率域,给出Uwc(ω)和Uic(ω),计算Uwc(ω)和Uic(ω)之间的关联函数F(ω)= Uic(ω)/ Uwc(ω), 再将F(ω)转换到时间域,即为uwc(t)和uic(t)之间的转换函数f(t)。
(3) 利用转换函数f(t)对实验测量的样品/窗口界面的粒子速度剖面uwe(t)做卷积,给出实验对应的原位粒子速度剖面uie(t):
uie(t)=uwe(t)∗f(t)=∫+∞−∞uwe(t-τ)f(τ)dτ (4) 具体计算过程中,可先计算频率域的实验原位速度以避开卷积的计算:
Uie(ω)=Uwe(ω)⋅F(ω) (5) 再将Uie(ω)做傅里叶逆变换,还原为实验对应的原位粒子速度剖面uie(t)。
图 2是我们采用数值试验,对转换函数法在处理复杂结构波形时的验证结果。先设定材料参数和加载波形,分别计算铜/LiF窗口界面速度曲线和原位速度曲线,再以计算的界面速度曲线作为“实验”的速度曲线并对其进行转换函数还原,将还原结果和计算的原位结果进行比较,发现还原的结果和计算结果完全吻合,表明该方法对复杂结构的速度波形具有良好的适用性。
在实际过程中,考虑到材料强度、粘性耗散等因素,很难做到计算的界面速度波形和实验结果完全吻合,因此需对转换函数方法的健壮性进行考核,即当计算的速度波形和实验速度波形存在一定的偏差时,采用转换函数计算的原位速度是否可靠。图 3给出了采用未考虑强度效应的计算波形对考虑了强度效应的“实验”波形进行近似,转换函数方法计算的原位速度波形和真值的比较。由于强度效应只是导致计算和“实验”速度波形在峰值位置出现较明显的偏差,因此对还原的原位速度影响不大。图 4分别为计算的速度幅值相对“实验”结果偏差10%和计算波形的脉宽相对“实验”结果偏差5%时,采用转换函数方法计算的原位粒子速度与真值的比较。比较结果表明速度偏差10%,脉宽偏差5%时,转换函数方法仍具有较好的适用性。此外,我们还计算了不同窗口阻抗匹配以及自由面情形下的原位速度还原,均获得了满意的结果。
3. 斜波压缩实验数据处理
以磁驱动斜波压缩强度测量实验结果为例,联合使用正向Lagrange方法和转换函数方法对实验结果进行分析,分析结果如图 5所示。图 5(a)给出了台阶靶的自由面速度曲线,对实验测量的自由面速度曲线做1/2近似,以此获得的原位速度曲线做正向数据处理,给出CL-u曲线如图 5(b)所示。由图 5(b)可知,给出加载段体波声速的线性拟合为CL= C0+2λu=3.34+2.55u,由此给出Grüneisen状态方程的C0=3.34 km/s,λ=1.27,将其带入反积分程序[21],计算加载界面的压力和速度历史,并给出Grüneisen状态方程的参数优化值。以反积分提供的加载界面压力(或速度)边界为基础,正向计算给出样品自由面的速度剖面,要求计算的界面速度曲线和实验结果尽量的接近;同时正向计算可给出样品厚度位置的原位速度剖面,计算结果如图 5(c)所示。再根据计算的界面速度和原位速度,采用转换函数方法,对实验测量的自由面速度进行还原,获得的原位速度如图 5(d)所示。利用实验结果的原位速度,正向计算给出加载-卸载过程中材料的CL-u曲线如图 5(e)所示。
由图 5(e)可见,采用转换函数方法进行数据处理获得的声速在加载末期出现了下降,这体现了加载后期应变率的剧烈变化以及加载波形衰减对声速计算的影响。采用转换函数方法计算的卸载声速相对自由面1/2近似计算结果偏小约8%,转换函数方法计算的卸载时弹性纵波声速的最大值和理论结果更为接近。根据实验测得的加载-卸载过程中拉氏声速的变化,即可参照文献[15]计算斜波压缩下的材料强度。
4. 结论
将Lagrange方法和转换函数方法在斜波压缩实验数据的正向处理中成功进行了应用,建立了斜波压缩实验数据处理的新流程,获得了可靠的实验结果。该数据处理方法的建立,将有效减小以往斜波压缩实验强度数据的计算误差,对强度实验数据的分析具有重要的作用。
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混凝土材料参数 密度/(kg·m–3) 弹性模量/GPa 泊松比 初始抗拉极限/MPa 抗剪极限/MPa 断裂韧度/(N·m–1) 剪切保持力 2 500 30 0.2 4.02 21 0.14 0.03 混凝土材料参数 钢筋材料参数 体积黏度 压屈应力/MPa 弹性模量/GPa 屈服应力/MPa 硬化模量/GPa 失效应变 0.72 42 200 335 10 0.75 表 2 冰材料模型参数
Table 2. Material parameters of ice
密度/(kg·m–3) 剪切模量/GPa 屈服应力/MPa 塑性硬化模量/GPa 体积模量/GPa 失效应变 截断应力/MPa 910 2.2 2.1 4.26 5.26 7.69×10–4 –4.0 表 3 水和空气介质材料参数
Table 3. Material parameters of water and air media
流体介质 密度/(kg·m–3) 截断压力/Pa 黏度系数/(N·s·m–2) C0 C1 C2 C3 C4 C5 E0/MPa V0 空气 1.184 5 –10 1.844×10−5 0 0 0 0 0.4 0.4 0.253 1.0 水 998.21 –1.0×10−5 1.790×10−3 1.0133×105 2.25×109 1.0 表 4 流冰-闸墩碰撞工况
Table 4. Flowing ice -pier collision conditions
工况 冰厚/m 冰温/℃ 冰速/(m·s–1) 冰体积/m3 冰压缩强度/MPa 1 0.3 –8 1.5 7.2 2.186 2 0.3 –8 1.5 14.4 2.186 3 0.3 –8 1.5 28.8 2.186 4 0.3 –8 1.5 64.8 2.186 5 0.3 –8 1.5 115.2 2.186 6 0.3 –2 1.5 64.8 1.123 7 0.3 –5 1.5 64.8 1.825 8 0.3 –8 1.5 64.8 2.186 9 0.3 –14 1.5 64.8 2.615 10 0.3 –20 1.5 64.8 2.889 -
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