A hyperbolic mathematical modeling for describing the transition saturated/unsaturated in a rigid porous medium

This work proposes a mathematical model to study the filling up of an unsaturated porous medium by a liquid identifying the transition from unsaturated to saturated flow and allowing a small super saturation. As a consequence the problem remains hyperbolic even when saturation is reached. This important feature enables obtaining numerical solution for any initial value problem and allows employing Glimm’s scheme associated with an operator splitting technique for treating drag and viscous effects. A mixture theory approach is used to build the mechanical model, considering a mixture of three overlapping continuous constituents: a solid (porous medium), a liquid (Newtonian fluid) and a very low-density gas (to account for the mixture compressibility). The constitutive assumption proposed for the pressure gives rise to a continuous function of the fluid fraction. The complete solution of the Riemann problem associated with the system of conservation laws, as well as four examples, considering all the four possible connections, namely, 1-shock/2-shock, 1-rarefaction/2-rarefaction, 1-rarefaction/2-shock and 1-shock/2-rarefaction are presented.     

KINEMATIC WAVE PROPERTIES OF ANISOTROPIC DYNAMICS MODEL FOR TRAFFIC FLOW

ＩｎｔｒｏｄｕｃｔｉｏｎＲｅｃｅｎｔｌｙｔｈｅａｕｔｈｏｒｓｐｒｅｓｅｎｔｅｄａｎｅｗｄｙｎａｍｉｃｓｍｏｄｅｌｆｏｒｔｒａｆｆｉｃｆｌｏｗ[1].Ｔｈｅｍｏｄｅｌｃｏｍｐｒｉｓｅｓａｃｏｎｔｉｎｕｕｍｅｑｕａｔｉｏｎａｎｄａｄｙｎａｍｉｃｓｅｑｕａｔｉｏｎ ｋ/ ｔ+ (ｋｕ) / ｘ=0 ,( 1 ) ｕ ｔ+ｕ ｕ ｘ=ｕｅ(ｋ) -ｕＴ +ａ ｕ ｘ,( 2 )ｗｈｅｒｅｋｉｓｔｒａｆｆｉｃｄｅｎｓｉｔｙ ;ｕｉｓｍｅａｎｓｐｅｅｄ ;ｘ ,ｔａｒｅｓｐａｃｅａｎｄｔｉｍｅｃｏｏｒｄｉｎａｔｅｓｒｅｓｐｅｃｔｉｖｅｌｙ .Ｔｉｓｒｅｌ…     

Basset力研究进展与应用分析

Basset力为两相流中颗粒与流体存在相对加速度时所产生的一种非恒定气动力 ,以往对其进行了大量的实验研究、理论分析和数值模拟。本文通过对Basset力研究文献的综述 ,分析并归纳了各种不同两相流动问题中该力的影响情况 ,得到的结论是 :对于气泡在液体内的流动问题 ,当气泡运动的脉动频率很大或很小时可以忽略Basset力对其运动的影响 ;对于固体或液体颗粒在气体中的运动问题可以忽略Basset力的影响 ;而其它两相流动问题则需要根据具体问题的特点来决定是否考虑Basset力的影响 ,其中需要考察 :流体与颗粒密度差别 ,颗粒尺寸 ,流动特征时间和颗粒运动弛豫时间 ,相对加速度 (或减速度 )等因素。本文还探讨了Basset力研究的发展方向。     

Relaxation effects associated with the flow of a dense gas through a porous medium

Unsteady processes of gas and Newtonian liquid flow through porous media are usually described within the framework of the standard elastic regime model [1, 2]. At the same time, from general theoretical considerations it is clear that for fairly small characteristic times of variation of the pressure and the seepage velocity the elastic regime model loses its validity and more general relaxation flow models [3, 4] must be employed. It is therefore important to determine the limits of applicability of the elastic regime model. For this purpose the unsteady process of gas flow from one vessel to another through a porous medium has been investigated theoretically and experimentally for small pressure differences and absolute pressures up to 50 MPa. It is shown that the experimental results diverge sharply from the theoretical predictions based on the elastic regime model. It is therefore proposed that for unsteady processes a generalization of Darcy's law with a relaxation kernel be employed. From the results of the experiments it is possible to determine the parameters of the kernel characterizing the internal relaxation processes in the porous medium-dense gas system.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 105–113, January–February, 1991.     

高架路匝道附近的交叉口交通流分析

考虑高架路匝道附近的交叉口交通流问题．所采用的模型是经修正的一维管流交通流模型,在运动方程中引入了弛豫项．基于该模型,对上海市内环线的武宁路匝道附近的交通流进行了案例分析,着重对主干道上的右转车辆干扰效应进行了数值模拟,所得结果与实测数据相当符合．分析表明,右转车辆对主干道的“挤压”效应是引起某些交叉口交通拥塞的重要原因,而设置在繁华路口的高架路匝道加剧了这种拥塞状况。     

An extended car-following model accounting for the honk effect and numerical tests

In this paper, an extended car-following model is proposed to simulate traffic flow by considering the honk effect. The stability condition of this model is obtained by using the linear stability analysis. The phase diagram shows that the honk effect plays an important role in improving the stabilization of traffic system. The mKdV equation near the critical point is derived to describe the evolution properties of traffic density waves by applying the reductive perturbation method. Furthermore, the numerical simulation is carried out to validate the analytical results and indicates that the traffic jam can be suppressed efficiently via taking into account the honk effect.     

Wave features related to a mathematical model describing pulse transmission in a nerve fibre

In order to describe the signal transmission in a nerve fibre, we consider a non-linear mathematical model which takes into account several dissipative mechanisms. By assuming different orders of magnitude for the relaxation times associated with each of them, we carry out an asymptotic analysis pointing out the wave features in different situations.     

随机车辆冲击作用下简支梁桥疲劳可靠度评估

为了研究考虑随机车辆冲击效应的简支梁桥疲劳安全水平,提出了基于车-桥耦合振动与随机车流的桥梁疲劳应力谱模拟方法,并应用于疲劳可靠度评估。基于某高速公路桥梁动态称重数据建立随机车流模型,采用小样本车辆数据拟合桥梁等效疲劳应力范围的插值响应函数,最后由高斯混合模型拟合大样本随机车流作用于桥梁构件的疲劳应力谱。分析了25 m标准跨径简支T梁桥底部普通钢筋的疲劳应力谱,评估了考虑路面劣化与交通量增长的桥梁疲劳可靠度。数值分析结果表明,基于随机车流模拟的疲劳应力谱具有典型的多峰分布特征,包含了超载车辆产生的疲劳应力;车辆对桥梁的冲击效应致使等效疲劳应力放大系数略大于冲击系数,当路面等级为一般时,采用规范冲击系数将低估车辆冲击效应的疲劳损伤;路面劣化与交通量增长均会导致桥梁运营期内的疲劳可靠指标显著降低,由路面劣化导致车辆对简支梁桥的冲击效应不可忽略。     

Short Communication Finite Element Analysis of Visco-elastic Flow Under High Shear Rate Using the GSMAC-method

In the present work, we carry out a finite element analysis of visco-elastic flows for the multi-mode Giesekus model at high shear rales flow. We have already proposed a new numerical scheme suitable for the analysis of visco-elastic fluids in the previous paper. It is mainly composed of two parts: the MUSCL (Monotone Upstream-centered Scheme for Conservation Law)-TVD (Total Variation Diminishing) for the numerical analysis of the constitutive equation and the GSMAC (Generalized Simplified Maker and Cell)-FEM (Finite Element Method) for the momentum equation. We apply the new scheme for the flows through the contraction plane for the multi-mode Giesekus model that considers eight relaxation modes. It shows suitable matching with experimental data at low shear rates, and we confirm that the results are stable at high shear rates.     

含铝炸药爆轰驱动的非线性特征线模型

针对含铝炸药爆轰的非理想特性,提出了含铝炸药爆轰产物膨胀的局部等熵假设,建立含铝炸药爆轰驱动的非线性特征线模型,为研究含铝炸药爆轰产物的非等熵流动和膨胀做功提供了一种新的理论分析方法。设计了5、50 μm含铝炸药和含LiF炸药驱动0.5、1 mm厚金属板实验,通过激光位移干涉仪测试金属板运动的速度历程,再通过实验结果计算得到铝粉在爆轰产物中的反应度变化规律,结合含铝炸药爆轰产物的非线性特征线模型,理论计算了含铝炸药驱动金属板的速度历程。对比理论与实验结果,理论方法能够很好地描述铝粉二次反应对炸药做功能力的贡献,同时验证了含铝炸药爆轰驱动的非线性特征线模型的正确性。     

Relaxation of a fluidized bed to the state of a continuous medium

The kinetic equation proposed in [1,2] for describing the behavior of a system of particles in a gas flow differs from the usual Boltzmann equation with respect to the additional terms that take into account random variations of the particle velocity under the influence of the flow. As shown in [2], the collision operator and the Brownian-type operator in the starting kinetic equation describe essentially different simultaneous physical processes of change of state of the particle system: equalization of the mean kinetic energy of the particles and change of energy due to the action of the viscous forces associated with the suspending flow. Therefore the method of solving the kinetic equation used in [2], a direct generalization of the Chapman-Enskog method of solving the kinetic equation it is necessary to investigate method of solving the kinetic equation it is necessar y to investigate the relaxation processes in the system. Moreover, the relaxation of systems of the fluidized-bed type to the continuum state is also of independent interest in connection with the analysis of fast processes in the system, i.e., processes with a characteristic duration of the order of the mean free time.     

大城市高架路实测数据分析与交通流模型研究

对上海市中心延安高架路一个路段交通流进行长时间录像拍摄,提取到``车速-车头间距'有效数据26000余对. 应用该批实测数据,对多种常见交通流速密关系模型进行比较研究后发现,一维管流模型在我国高速道路交通流参数计算中具有优势. 提出采用变参数一维管流模型刻画交通流非线性特征的基本方法.      

Feedback control for the lattice hydrodynamics model with drivers’ reaction time

In this paper, a new lattice hydrodynamic model (LH model) of traffic flow under consideration of reaction time of drivers and a corresponding feedback control scheme are proposed. Based on the model, stability analysis is conducted through linear stability analysis of transfer function. The obtained phase diagram indicates that the reaction time of driver can affect the instability region of traffic flow. Under the action of a feedback control, the unstable region is shrunken to reach suppressing jams. The numerical simulations are performed to validate the effect of reaction time of driver in the new LH model. The study results confirm that the reaction time of driver significantly affects the unstability of traffic system, and the feedback control can suppress traffic jams. Furthermore, it is found that the traffic system from the chaotic traffic state to periodic steady one is successfully realizing the control of traffic system.     

A new lattice model of the traffic flow with the consideration of the driver anticipation effect in a two-lane system

In this paper, a new lattice model of the traffic flow is proposed with the consideration of the driver anticipation effect for a two-lane system. The linear stability condition is derived by employing linear stability analysis. The analytical result shows that the driver anticipation effect can improve the stability of the traffic flow in a two-lane system. The mKdV equation near the critical point is obtained to describe the propagating behavior of a traffic density wave with the perturbation method. The simulation results are also in good agreement with the analytical results, which show that the traffic jam can be suppressed efficiently when the driver anticipation effect is considered in a two-lane system.     

Generalized macroscopic traffic model with time delay

The effect of delay or reaction time on traffic flow dynamics has been investigated widely in the literature using microscopic traffic models. Recent studies using second-order Payne-type models have shown analytically that, on a macroscopic scale, time delay does not contribute to whether traffic instabilities occur. This paper will attempt to show that it all depends on the (macroscopic) model used for the analysis that delay does have effect on traffic instabilities or not. To this end, we will formulate a generalized (linear) stability condition for a second-order macroscopic model with delay and investigate analytically the effect of such delay on traffic instabilities in some specific macroscopic models. It is found that the choice of the equilibrium speed function in a (second order) macroscopic model will determine how delay affects such (linear) stability condition     

Multi-mode solitons in a long-short range traffic lattice model with time delay

We consider a new form of solutions of a special lattice model for traffic system. By analyzing nearest sites’ interactions, time delay, and bumpy effects, we deduce the bifurcation lines and surfaces for stable and unstable regions and show how they vary as parameters vary. It shows that keeping other conditions unchanged, as the incoming flow increases, the traffic flow becomes unstable, opposite to when outgoing flow increases, it becomes stable. Besides, considering delayed optimal flow, multiple sites effect or artificial parameters can also help stabilize the traffic road condition. Moreover, by putting it into the framework of mKdV equations, we obtain the kink–antikink solitons involving all parameters, which show the feature of the traffic congestion. The result is original, and our model in differential or difference form can be reduced into the previous ones by choosing appropriate parameters. Since the optimal velocity function we considered involves finitely or infinitely many sites, the density waves can be in multi-mode and high dimension forms and can also be quasi-periodic, we show a new feature of the traffic lattice system.

     

Experimental study of flow structures in a large range downstream the spacer grid in a 5 × 5 rod bundle using TR-PIV

In this paper, the time-resolved particle image velocimetry (TR-PIV) and match index refractive (MIR) techniques were used to study the flow field in a large range (0 – 22 D_h) downstream a spacer grid (SG) in a 5 × 5 rod bundle channel at different Reynolds number. The sodium chloride solution (1%) is used as the working fluid to reduce the refractive index error of fluorinated ethylene propylene (FEP) and water. The proper orthogonal decomposition (POD) background removal technique was used to minimize the FEP reflection. These methods greatly reduced the interference of background noise and improved the accuracy of cross-correlation calculation. For TR-PIV velocity fields downstream of the mixing vanes, time-averaged, statistical, spectral, and cross-correlation analysis were performed for the instantaneous full-field experimental data. The transport characteristics of coherent structures in different subchannels of rod bundles are calculated and discussed. The results show that the SG caused a relatively large transverse velocity and reduces the axial velocity. With the increase of the Reynolds number, the SG promotes the generation of transverse flow and has a great resistance to the axial flow. There is relatively large turbulence intensity downstream of the SG due to the mixing effect. The attenuation of transverse turbulence intensity component is slower than the axial component. Moreover, spectrum analysis shows that cross-arranged mixing vanes will generate periodic vortices but single mixing vane will not. These periodic vortices gradually propagate downstream along the inner subchannel and dissipate in the gap subchannel due to the effect of viscosity. The cross-correlation analysis shows that the mixing effect of the SG will reduce the scale of the coherent structure, and increase the convection velocity. The results of current research are helpful for understanding the strong anisotropic turbulence in the rod bundle channel with SG. Finally, the experimental results can be utilized to benchmark the applicability of turbulence models under different Reynolds number and the performance of partially averaged Naiver–Stokes or multiple RANS algorithms downstream of the SG.     

基于有限差分-谱方法的分数阶Burgers流体的非稳态驻点流动

研究了分数阶Burgers流体通过拉伸平板的非稳态驻点流动问题。将分数阶导数引入Burgers流体模型可以更好地模拟流动过程,但也增加了模型的复杂性和求解难度。首次运用有限差分-谱方法求解分数阶Burgers流体模型,离散格式构造简单有效。采用谱方法对控制方程中的空间项进行离散,利用有限差分方法分别结合L-1和L-2算法离散控制方程中的时间项,给出了两种离散格式,并且通过构造数值算例证明了离散格式的收敛性。结果表明,在靠近平板处,速度随着分数阶导数的增加而减小,而无穷远处的流体速度呈现出相反的趋势,体现了分数阶导数的记忆特性。此外,雷诺数越小,流体的粘度越大,导致流体速度越大。由于松弛时间参数的松弛特性,靠近平板处松弛时间参数对速度分布有抑制作用,远离平板处松弛时间促进流体流动。     

Transient Couette flows of Oldroyd's fluids under imposed torques

We study the transient Couette flow of an Oldroyd fluid that fills the gap between two circular cylinders when a constant torque is suddenly applied to the inner cylinder, the outer one being kept motionless. Contrarily to most former studies, the inertia of the moving boundary is not neglected. We give the exact solutions of this problem for a wide class of initial conditions and we present a rigorous asymptotic analysis for small gap devices when the initial state is stationary. The case of Grade 2 fluids is also considered and treated. We also show in some experimental tests, that the knowledge of the relaxation curve of the angular velocity of the rotor can be used to identify the parameters of the model.