幂律流体在多孔介质中径向渗流的分形模型

基于分形理论及毛细管模型,本文研究了非牛顿幂律流体在各向同性多孔介质中径向流动问题,推导了幂律流体径向有效渗透率的分形解析表达式．研究结果表明,幂律流体径向有效无量纲渗透率模型和Chang and Yortsos’s模型吻合很好;同时还得出幂律流体径向有效渗透率随孔隙率、幂指数的增加而增加,随迂曲度分形维数的增加而减少．     

粗糙表面接触力学问题的重新分析

为了克服基于统计学参数的接触模型的尺度依赖性以及现有接触分形模型推导过程中初始轮廓表征受控于接触面积或取样长度的不足,基于粗糙表面轮廓分形维数$D$、尺度系数$G$ 和最大微凸体轮廓基底尺寸$l$,建立了新的粗糙表面接触分形模型,探讨了微凸体变形机制、粗糙表面的真实接触面积和接触载荷的关系,揭示了接触界面的孔隙率和真实接触面积随端面形貌、表面接触压力等参数变化的规律,给出了不同形貌界面被压实的最大变形量. 结果表明:微凸体变形从弹性变形开始,并随着平均接触压力$p_{\rm m}$ 的增大逐步向弹塑性变形和完全塑性变形转变;接触界面的初始孔隙率$\phi_{0}$ 随$D$ 的增大而增大,压实孔隙所需要的最大变形量$\delta $ 也随之增大;接触压力$p_{\rm c}$ 增大,孔隙率$\phi$ 减小,并随着$D$ 的增大和$G$ 减小,$\phi$ 快速减小,直至填实,变为零;$D$ 较小时,$G$ 的增大对真实接触面积的增大影响较小;$D$ 较大时,$G$ 的增大对真实接触面积的增大作用明显. 研究成果为端面摩擦副的润滑与密封设计提供了理论基础.      

不同壁面取向下超疏水平面直轨道上的气泡滑移

利用特定几何分布的超疏水表面实现气泡定向输运在矿物浮选和生物孵化等领域具有广阔的应用前景, 对平面直线超疏水轨道而言, 其壁面取向是相关工程结构的关键参数, 但超疏水壁面取向对倾斜壁面气泡滑移的影响尚不明确. 本文采用高速阴影成像系统研究了不同壁面取向($-90^\circ\leqslant \beta \leqslant 90^\circ$)及轨道倾角($45^\circ\leqslant \alpha \leqslant 75^\circ$)下, 气泡($D_{eq}=2.4$ mm, $Re=500$ $\sim$ 700, $We=7$ $\sim$ 13)在轨道宽度为2 mm的超疏水直线轨道上的运动特性. 气泡在轨道上的滑移近似为匀速, 形状为具有多脊的半子弹型. 根据气液界面波动程度的不同, 滑移气泡可分为波动型和稳定型, 稳定型气泡只在较小倾角且较大方位角时出现($45^\circ\leqslant \alpha < 70^\circ$, $| \beta | \geqslant 45^\circ$). 根据倾角不同, 滑移速度关于$\beta $有2种变化规律: 当$\alpha \leqslant 65^\circ$, 气泡滑移速度近似为关于$\beta =0^\circ$ 的单峰分布($\beta =0^\circ$时, 气泡滑移速度最大); 当$\alpha \geqslant 70^\circ$, 气泡滑移速度在不同的方位角下基本保持稳定. 气泡的最大滑移速度可达0.66 m/s ($\beta =0^\circ$, $\alpha =70^\circ$), 远大于相同尺度的自由上升气泡($\approx0.25$ m/s), 这主要是壁面浸润性分布和惯性力的耦合效应所致. 轨道取向(方位角$\beta )$及轨道倾角($\alpha )$通过改变气泡沿轨道方向的驱动力和气泡迎风面积影响气泡的滑移速度和气液界面稳定性.      

一个改进的电磁波传输激波管实验

在中国科学院力学研究所$\varPhi $ 800 mm高温低密度激波管上进行电磁波在等离子体中传输机理研究时,低密度和强激波条件下,由于气体解离和电离等非平衡过程,使得激波后2区宽度显著减小;同时由于边界层效应造成激波衰减和接触面加速,使得激波后2区长度进一步减小.这两个效应导致激波管2区实验观测 时间减小,2区气体处于非平衡状态,增加了观察数据的不稳定性和数据分析的难度.本文提出在$\varPhi 800 $ mm高温低密度激波 管中采用氩气(Ar)和空气(Air)混合气替代纯空气作为激波管实验介质气体.利用Ar不解离和难电离的特性,减小激波前后压缩比,从而 增加激波后2区实验时间和气体长度. 采用Langmuir 静电探针和微波透射诊断技术测量激波后电子密度,同时利用探针测量激波后2区实验时间.结果显示,在Ar+Air混合气实验中,激波波后电子密度可达与纯Air同样的10$^{13}$cm$^{ - 3}$量级.在与纯Air相同的电子密度和碰撞频率条件下,采用95%Ar+5%Air和90%Ar+10%Air两种混合气,激波后2区实验时间和气体长度约为纯Air条件下的5$\sim $10倍,其中2区实验时间为300$\sim $800 $\mu$s,2区气体长度1$\sim $1.5 m.在$\varPhi $800 mm激波管中采用Ar+Air介质气体进行电磁波传输实验,获得了比在纯Air介质中与理论预测更一致的结果.      

低雷诺数沟槽表面湍流/非湍流界面特性的实验研究

湍流/非湍流界面是流动中湍流和无旋流的边界,其相关研究在加深对湍流与无旋流之间的物质、动量和能量交换的理解有重要意义.本文采用时间解析的二维粒子图像测速技术,分别对零压梯度光滑、顺流向锯齿形沟槽表面平板在不同雷诺数下对湍流/非湍流界面的几何特征及动力学特性进行了实验研究.实验雷诺数为$Re_{\tau } =400\sim1000$.本文采用了湍动能准则对湍流/非湍流界面进行了识别,并分析界面高度分布、分形特征及界面附近的条件平均速度和涡量.结果表明在不同雷诺数下, 无论是光滑壁面还是沟槽壁面,界面平均高度在0.8 $\sim$ 0.9$\delta_{99} $附近. 对于沟槽壁面而言,减阻时对应的界面高度的概率密度分布与光滑壁面基本一致, 均遵循正态分布,而当阻力增大时, 界面高度分布偏离正态分布出现正的偏度. 在本实验情况下,界面分形维度、跨界面速度跳变均会随着雷诺数增大而增大. 此外,不同壁面情况下无量纲条件平均涡量在界面附近的分布相近,而界面附近无量纲速度梯度最大值近似为常数.      

垂直壁面附近上升单气泡的弹跳动力学研究

采用高速摄影技术结合阴影法,对静止水中垂直壁面附近上升单气泡运动进行实验研究,对比气泡尺度及气泡喷嘴与壁面之间的初始无量纲距离 ($S^{\ast}$)对气泡上升运动特性的影响,分析气泡与壁面碰撞前后,壁面效应与气泡动力学机制及能量变化规律.结果表明,对于雷诺数$Re \approx 580 \sim 1100$,无量纲距离$S^{\ast } <2 \sim3$时,气泡与壁面碰撞且气泡轨迹由无约束条件下的三维螺旋转变成二维之字形周期运动;当$S^{\ast } >2 \sim3$时,壁面效应减弱,有壁面约束的气泡运动与无约束气泡运动特性趋于一致.气泡与壁面碰撞前后,壁面效应导致横向速度峰值下降为原峰值的70%,垂直速度下降50%;气泡与壁面碰撞前,通过气泡中心与壁面距离($x/R$)和修正的斯托克斯数相关式可预测垂直速度的变化规律.上升气泡与壁面碰撞过程中,气泡表面变形能量单向传输给气泡横向动能,使得可变形气泡能够保持相对恒定的弹跳运动.提出了气泡在与壁面反复弹跳时的平均阻力系数的预测模型,能够很好地描述实验数据反映出的对雷诺数${Re}$、韦伯数${We}$和奥特沃斯数${Eo}$等各无量纲参数的标度规律.      

周期性多孔材料等效剪切模量与尺寸效应研究

提出了以圆筒扭转力学模型为基础, 预测周期性多孔材料等效剪切模量及其研究尺寸效 应的一种简单有效计算方法. 以方形孔和圆形孔两种典型多孔材料为例进行了数值计算求解; 同时, 建立了几何参数随体胞尺寸缩放因子$n$的解析关系, 证明了两种构型的周期性多孔材 料的等效剪切模量均随尺寸缩放因子$n$的增大而减小. 当$n \to \infty $时, 即体胞尺寸相对整体结构无限小时, 多孔材料的等效剪切模量趋近收敛于一个恒定值; 当体胞的材料体分比增大时, 多孔材料等效剪切模量也随之增大. 此外, 依据周 期性多孔材料的结构对称特性, 使用体胞子结构有限元计算模型进行等效剪切模量及其尺寸 效应的预测, 极大地提高了计算效率.     

16MnR钢缺口试样解理断裂行为研究

研究了低合金热轧钢16MnR缺口试样在$-196\,{^\circ}$C和$-130\,{^\circ}$C的解理断裂机 理. 拉伸试验、单、双缺口四点弯曲实验、断口形貌观察以及有限元分析结果表明, 缺口试 样发生解理断裂时均起裂于夹杂物粒子, 一种位于缺口根部前端(IC型), 另一种位于距缺口 根部较远的条形裂纹前端(SIC型); 且随温度升高, 起裂源的类型从$-196\,{^\circ}$C下的IC 型转变为$-130\,{^\circ}$C下的SIC型. 微裂纹均形核于夹杂物, 最终的断裂由铁素体晶粒尺 寸的微裂纹扩展控制. 缺口试样IC型解理断裂遵循裂纹形核条 件$\varepsilon_{\rm p} \ge \varepsilon_{\rm pc}$和裂纹扩展条件$\sigma_{yy} \ge \sigma_{f}$, 而SIC型解理断裂条件则演化为$\varepsilon_{\rm p}+\varepsilon_{\rm ps} \ge \varepsilon_{\rm pc}$和$\sigma_{yy} +\sigma_{yy{\rm s}} \ge \sigma_{f}$.     

天然弯曲河流的三维数值模拟

对Cartesian坐标系下的RANS方程进行三维$\xi$-$\eta$-$\zeta$坐标变换，建 立了非正交三维曲线坐标下弯曲河流的标准$k$-$\varepsilon$湍流模型. 对自由水面 的模拟采用``改进的刚盖假定'，河床和岸壁阻力的模拟采用壁面函数方法. 模型通 过具有实验数据的实验室连续弯曲水槽进行验证，模拟的流速值与实验数 据吻合良好，将模型应用于天然连续弯曲河流的流场计算，给出了表层和底层流速 矢量场和11个断面二次环流矢量图，显示该模型具有模拟天然弯曲河流的能力.     

完整岩石拉压应力状态下的张裂破坏准则

一点的应力状态可由3个主应力$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$来表示, 当规定主应力以压为正时, 沿最大主应力$\sigma_{1}$方向将产生收缩变形, 若中间主应力$\sigma_{2}$和最小主应力$\sigma_{3}$都远小于$\sigma_{1}$, 则沿$\sigma_{2}$和$\sigma_{3}$方向会产生横向扩张变形, 当横向扩张变形达到一定极限时, 将会在平行于$\sigma _{1}$的方向产生张裂破坏. 如何建立这种张裂破坏的强度准则目前尚缺乏研究, 最大拉应变理论(第二强度理论)有时被用来解释张裂破坏, 但最大拉应变理论难以应用于三向受力状态. 本文分别用$\varepsilon_{1}$, $\varepsilon_{2}$表示最大张应变和次大张应变, 则最大拉应变理论认为当$\varepsilon_{1}$达到单向拉伸屈服应变时, 材料将产生破坏. 而本文将根据$\varepsilon_{1}+\varepsilon_{2}$之和达到极限值$\varepsilon_u$来建立张裂破坏准则. 可以证明$\varepsilon_{1} +\varepsilon_{2}$所表示的是$\sigma_{1}$主平面的面积增长率. 当$\sigma_{3}<\sigma_{2} \ll \sigma_{1}$时, 大部分岩石都具有脆性破坏的特点, 所以可将破坏前的岩石视为满足广义胡克定律的线弹性材料, 这样用$\varepsilon_{1}$, $\varepsilon_{2}$表示的强度准则可通过$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$来表示. 在这个过程中还可考虑岩石在拉伸和压缩时具有不同弹性参数和强度的特点, 并可通过单向拉伸和单向压缩的破坏状态来确定$\varepsilon_u$. 不管$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$是压应力, 还是拉应力, 或者$\sigma_{1}$, $\sigma_{2}$, $\sigma_{3}$中有拉有压的情形, 基于$\varepsilon_{1} +\varepsilon_{2} =\varepsilon_u$都可建立相应的强度准则. 所建立的准则可以反映中间应力$\sigma_{2}$对强度的影响规律, 通过建立的强度准则还可以证明: 静水拉力能引起屈服, 而静水压力不能产生屈服; 压缩破坏能使塑性体积增大, 其结果比Mohr-Coulomb准则更能反映实际情形. 并通过拉压应力状态下的试验数据验证了所建立的强度准则, 所得理论计算结果和已有的试验数据吻合得很好. 通过提出的强度准则和圆盘劈裂的试验结果, 可获得更为可靠的岩石单轴抗拉强度.      

A Discussion of the Effect of Tortuosity on the Capillary Imbibition in Porous Media

In the past decades, there was considerable controversy over the Lucas–Washburn (LW) equation widely applied in capillary imbibition kinetics. Many experimental results showed that the time exponent of the LW equation is less than 0.5. Based on the tortuous capillary model and fractal geometry, the effect of tortuosity on the capillary imbibition in wetting porous media is discussed in this article. The average height growth of wetting liquid in porous media driven by capillary force following the [`(L)] _s(t) ~ t^1/2D_T{\overline L _{\rm {s}}(t)\sim t^{1/{2D_{\rm {T}}}}} law is obtained (here D _T is the fractal dimension for tortuosity, which represents the heterogeneity of flow in porous media). The LW law turns out to be the special case when the straight capillary tube (D _T = 1) is assumed. The predictions by the present model for the time exponent for capillary imbibition in porous media are compared with available experimental data, and the present model can reproduce approximately the global trend of variation of the time exponent with porosity changing.     

An Analytic Solution for the Frontal Flow Period in 1D Counter-Current Spontaneous Imbibition into Fractured Porous Media Including Gravity and Wettability Effects

Including gravity and wettability effects, a full analytical solution for the frontal flow period for 1D counter-current spontaneous imbibition of a wetting phase into a porous medium saturated initially with non-wetting phase at initial wetting phase saturation is presented. The analytical solution applicable for liquid–liquid and liquid–gas systems is essentially valid for the cases when the gravity forces are relatively large and before the wetting phase front hits the no-flow boundary in the capillary-dominated regime. The new analytical solution free of any arbitrary parameters can also be utilized for predicting non-wetting phase recovery by spontaneous imbibition. In addition, a new dimensionless time equation for predicting dimensionless distances travelled by the wetting phase front versus dimensionless time is presented. Dimensionless distance travelled by the waterfront versus time was calculated varying the non-wetting phase viscosity between 1 and 100 mPas. The new dimensionless time expression was able to perfectly scale all these calculated dimensionless distance versus time responses into one single curve confirming the ability for the new scaling equation to properly account for variations in non-wetting phase viscosities. The dimensionless stabilization time, defined as the time at which the capillary forces are balanced by the gravity forces, was calculated to be approximately 0.6. The full analytical solution was finally used to derive a new transfer function with application to dual-porosity simulation.     

微重力下成一定夹角平板间的表面张力驱动流动的研究

空间微重力环境中,由于重力基本消失,表面张力等次级力发挥主要作用,流体行为与地面迥异,因此有必要深入探究微重力环境中的流体行为规律和特征.板式贮箱利用板式组件在微重力环境中对流体进行管理,从而为推力器提供不夹气的推进剂,这对航天器精确进行姿态控制、轨道调整具有重要意义.板式组件中常包含成一定夹角的平板结构,比如蓄液叶片...     

Spontaneous Inertial Imbibition in Porous Media Using a Fractal Representation of Pore Wall Rugosity

Considering the separable phenomena of imbibition in complex fine porous media as a function of timescale, it is noted that there are two discrete imbibition rate regimes when expressed in the Lucas–Washburn (L–W) equation. Commonly, to account for this deviation from the single equivalent hydraulic capillary, experimentalists propose an effective contact angle change. In this work, we consider rather the general term of the Wilhelmy wetting force regarding the wetting line length, and apply a proposed increase in the liquid–solid contact line and wetting force provided by the introduction of surface meso/nanoscale structure to the pore wall roughness. An experimental surface pore wall feature size regarding the rugosity area is determined by means of capillary condensation during nitrogen gas sorption in a ground calcium carbonate tablet compact. On this nano size scale, a fractal structure of pore wall is proposed to characterize for the internal rugosity of the porous medium. Comparative models based on the Lucas–Washburn and Bosanquet inertial absorption equations, respectively, for the short timescale imbibition are constructed by applying the extended wetting line length and wetting force to the equivalent hydraulic capillary observed at the long timescale imbibition. The results comparing the models adopting the fractal structure with experimental imbibition rate suggest that the L–W equation at the short timescale cannot match experiment, but that the inertial plug flow in the Bosanquet equation matches the experimental results very well. If the fractal structure can be supported in nature, then this stresses the role of the inertial term in the initial stage of imbibition. Relaxation to a smooth-walled capillary then takes place over the longer timescale as the surface rugosity wetting is overwhelmed by the pore condensation and film flow of the liquid ahead of the bulk wetting front, and thus to a smooth walled capillary undergoing permeation viscosity-controlled flow.     

Fractal Prediction Model of Spontaneous Imbibition Rate

By utilizing fractal dimension as one of the parameters to characterize rocks, a mathematical model was derived to predict the production rate by spontaneous imbibition. This fractal production model predicts a power law relationship between spontaneous imbibition rate and time. Fractal dimension can be estimated from the fractal production model using the experimental data of spontaneous imbibition in porous media. The experimental data of recovery in gas-water-rock and oil–water–rock systems were used to test the fractal production model. The rocks (Berea sandstone, chalk, and The Geysers graywacke) in which the spontaneous water imbibition experiments were conducted had different permeabilities ranging from 0.5 to over 1000 md. The results demonstrate that the fractal production model can match the experimental data satisfactorily in the cases studied. The fractal dimension data inferred from the model match were approximately equal to the values of fractal dimension measured using a different technique (mercury-intrusion capillary pressure) in Berea sandstone.     

Capillary bridges and capillary forces between two axisymmetric power–law particles

Capillary interactions are fundamentally important in many scientific and industrial fields. However, most existing models of the capillary bridges and capillary forces between two solids with a mediated liquid, are based on extremely simple geometrical configurations, such as sphere–plate, sphere–sphere, and plate–plate. The capillary bridge and capillary force between two axisymmetric power–law profile particles with a mediated constant-volume liquid are investigated in this study. A dimensionless method is adopted to calculate the capillary bridge shape between two power–law profile particles based on the Young–Laplace equation. The critical rupture criterion of the liquid bridge is shown in four forms that produce consistent results. It was found that the dimensionless rupture distance changes little when the shape index is larger than 2. The results show that the power–law index has a significant influence on the capillary force between two power–law particles. This is directly attributed to the different shape profiles of power–law particles with different indices. Effects of various other parameters such as ratio of the particle equivalent radii, liquid contact angle, liquid volume, and interparticle distance on the capillary force between two power–law particles are also examined.     

The Impact of Tides on the Capillary Transition Zone

The capillary transition zone, also known as the capillary fringe, is a zone where water saturations decrease with height above the water table/oil–water contact as a result of capillary action. In some oil reservoirs, this zone may contain a significant proportion of the oil in place. In groundwater assessments, the capillary fringe can profoundly affect contaminant transport. In this study, we investigated the influence of a tidally induced, semi-diurnal, change in water table depth on the water saturation distribution in the capillary fringe/transition zone. The investigation used a mixture of laboratory experiments, in which the change in saturation with depth was monitored over a period of 90 days, and numerical simulation. We show that tidal changes in water table depth can significantly alter the vertical water saturation profile from what would be predicted using capillary–gravity equilibrium and the drainage or imbibition capillary pressure curves.     

SPONTANEOUS CAPILLARY IMBIBITION MODEL IN TIGHT OIL RESERVOIRS 1)

部分致密油井压后关井一段时间，压裂液返排率普遍低于30%，但是致密油气井产量反而越高，这与压裂液毛细管力渗吸排驱原油有关。然而，致密油储层致密，物性差，渗流机理复杂，尚没有形成统一的自发渗吸模型。本文基于油水两相非活塞式渗流理论，建立了压后闷井期间压裂液在毛细管力作用下自发渗吸进入致密油储层的数学模型，采用数值差分方法进行求解，并分析了相关影响因素。结果显示渗吸体积、渗吸前缘移动距离与渗吸时间的平方根呈线性正相关关系，与经典Handy渗吸理论模型预测结果一致，说明毛细管力自发渗吸模型可靠性较高。数值计算结果表明毛细管水相扩散系数是致密储层自发渗吸速率的主控参数，毛细管水相扩散系数越高，自发渗吸速率越大。毛细管水相扩散系数随着含水饱和度先增加后减小；随着束缚水饱和度、油相和水相端点相对渗透率增加而增加；随着相渗特征指数、油水黏度比和残余油饱和度增加而减小。该研究有助于深入认识致密油储层压裂液渗吸机理，对优化返排制度、提高致密油井产量具有重要意义。     

Ensemble phase averaged equations for multiphase flows in porous media. Part 2: A general theory

Most models for multiphase flows in a porous medium are based on a straightforward extension of Darcy’s law, in which each fluid phase is driven by its own pressure gradient. The pressure difference between the phases is thought to be an effect of surface tension and is called capillary pressure. Independent of Darcy’s law, for liquid imbibition processes in a porous material, diffusion models are sometime used. In this paper, an ensemble phase averaging technique for continuous multiphase flows is applied to derive averaged equations and to examine the validity of the commonly used models. Closure for the averaged equations is quite complicated for general multiphase flows in a porous material. For flows with a small ratio of the characteristic length of the phase interfaces to the macroscopic length, the closure relations can be simplified significantly by an approximation with a second order error in this length ratio. This approximation reveals the information of the length scale separation obscured during an averaging process and leads to an equation system similar to Darcy’s law, but with additional terms. Based on interactions on phase interfaces, relations among closure quantities are studied.     

A geometrical model for numerical simulation of capillary imbibition in sedimentary rocks

The cylindrical model is discussed and a new tube model is proposed to describe capillary imbibition kinetics in porous sedimentary rocks. The tube consists of a periodic succession of a single hollow spherical element of which the geometry is defined by the sphere radius and the sphere access radius. These two parameters are estimated experimentally for four rock types from their specific surface areas. Introducing those parameters in the model capillary imbibition kinetics, parameters are calculated and compared with the experimental ones. A direct relation between imbibition kinetics and specific surface area has been pointed out.