One-dimensional consolidation of double-layered soil with non-Darcian flow described by exponent and threshold gradient

Based on non-Darcian flow law described by exponent and threshold gradient within a double-layered soil, the classic theory of one-dimensional consolidation of double-layered soil was modified to consider the change of vertical total stress with depth and time together. Because of the complexity of governing equations, the numerical solutions were obtained in detail by finite difference method. Then, the numerical solutions were compared with the analytical solutions in condition that non-Darcian flow law was degenerated to Dary's law, and the comparison results show that numerical solutions are reliable. Finally, consolidation behavior of double-layered soil with different parameters was analyzed, and the results show that the consolidation rate of double-layered soil decreases with increasing the value of exponent and threshold of non-Darcian flow, and the exponent and threshold gradient of the first soil layer greatly influence the consolidation rate of double-layered soil. The larger the ratio of the equivalent water head of external load to the total thickness of double-layered soil, the larger the rate of the consolidation, and the similitude relationship in classical consolidation theory of double-layered soil is not satisfied. The other consolidation behavior of double-layered soil with non-Darcian flow is the same as that with Darcy's law.

The Construction Method for Solving Radial Flow Problem through the Homogeneous Reservoir

On the basis of similar structure of solutions of ordinary differential equation (ODE) boundary value problem, the similar construction method was put forward by solving problems of fluid flow in porous media through the homogeneous reservoir. It is indicate that the pressure distribution of dimensionless reservoir and bottom hole in Laplace space, which take on the radial flow, also shows similar structure, and the internal relationship between the above solutions were illustrated in detail.

Homogeneous Plastic Flow of Fully Amorphous and Partially Crystallized Zr_(41.2)Ti_(13.8)Cu_(12.5)Ni_(10)Be_(22.5) Bulk Metallic Glass

The homogeneous plastic flow of fully amorphous and partially crystallized Zr(41.2)Ti(13.8)Cu(12.5)Ni(10)Be(22.5) bulk metallic glass (Vitl) has been investigated by compression tests at high temperatures in supercooled liquid region. Experimental results show that at sufficiently low strain rates, the supercooled liquid of the fully amorphous alloy reveals Newtonian flow with a linear relationship between the flow stress and strain rate. As the strain rate is increased, a transition from linear Newtonian to nonlinear flow is detected, which can be explained by the transition state theory. Over the entire strain rate interval investigated, however, only nonlinear flow is present in the partially crystallized alloy, and the flow stress for each strain rate is much higher. It is found that the strain rate-stress relationship for the partially crystaltized alloy at the given temperature of 646 K also obeys the sinh law derived from the transition state theory, similar to that of the initial homogeneous amorphous alloy. Thus, it is proposed that the flow behavior of the nanocrystalline/amorphous composite at 646 K is mainly controlled by the viscous flow of the remaining supercooled liquid.

MOLECULAR MODEL AND FLOW CALCULATION:Ⅰ.THE NUMERICAL SOLUTIONS TO MULTIBEAD-ROD MODELS INHOMOGENEOUS FLOWS

The Galerkin method is used to solve the diffusion equation of the distribution function in configurational space for a multibead-rod model,and the dimensionless components of the extra stress tensor are then calculated by means of the expression of ensemble average.The material functions for steady-state shear flow and uniaxial flow and the mechanical properties of rigid-rodlike molecule suspen- sions in superposed flows are obtained numerically.The results indicate that it is promising to employ the mu ltibead-rod models without the constitutive equation in numerical simulations of flows of suspensions.

Solution Method for Singular Initial Value Problems of One-dimensional Steady Transonic Flow in a Dual-mode Scramjet

Singular initial value problems arise in solving one-dimensional steady transonic flow of dualmode scramjet. The existing solution method has the problems of large initial value errors in principles. This paper puts forward an improved algorithm based on variable transformation, and constructs a nonsingular one-dimensional steady transonic flow equation by defining a new variable. The improved algorithm can eliminate the singularity of the differential equation, and can solve the singular initial value problems of one-dimensional steady transonic flow of dual-mode scramjet.

Comparison of One-Dimensional Analysis with Experiment for CO₂Two-Phase Nozzle Flow

The aim of this study is to investigate CO2 two-phase nozzle flow in terms of both experimental and analytical aspects for the optimum design of two-phase flow nozzle of CO2 two-phase flow ejector. In the experiment, it is measured that the temperature profile in the stream-wise direction of a divergent-convergent nozzle through which CO2 in the supercritical pressure condition is blown down into the atmosphere. In the analysis, a one-dimensional model which assumes steady, adiabatic, frictionless, and equilibrium is proposed. In the convergent part of the nozzle the flow is treated as single-phase flow of liquid, whereas in the divergent part the flow is treated as separated two-phase flow with saturated condition. The analytical results indicate that the temperature and the pressure decrease rapidly in the divergent part, and the void fraction increases immediately near the throat. Although this analysis is quite simple, the analytical results can follow the experimental results well within this study.

Analysis of one-dimensional consolidation of soft soils with non-Darcian flow caused by non-Newtonian liquid

Based on non-Darcian flow caused by non-Newtonian liquid, the theory of one-dimensional (1D) consolidation was modified to consider variation in the total vertical stress with depth and time. The finite difference method (FDM) was adopted to obtain numerical solutions for excess pore water pressure and average degree of consolidation. When non-Darcian flow is degenerated into Darcian flow, a comparison between numerical solutions and analytical solutions was made to verify reliability of finite difference solutions. Finally, taking into account the ramp time-dependent loading, consolidation behaviors with non-Darcian flow under various parameters were analyzed. Thus, a comprehensive analysis of 1D consolidation combined with non-Darcian flow caused by non-Newtonian liquid was conducted in this paper.

Algebraic Calculation Method of One-Dimensional Steady Compressible Gas Flow

This paper describes a new method of calculation of one-dimensional steady compressible gas flows in channels with possible heat and mass exchange through perforated sidewalls. The channel is divided into small elements of a finite size for which mass, energy and momentum conservation laws are written in the integral form, assuming linear distribution of the parameters along the length. As a result, the calculation is reduced to finding the roots of a quadratic algebraic equation, thus providing an alternative to numerical methods based on differential equations. The advantage of this method is its high tolerance to coarse discretization of the calculation area as well as its good applicability for transonic flow calculations.

Diffusion Process of High Concentration Spikes in a Quasi-Homogeneous Turbulent Flow

When a mass spreads in a turbulent flow, areas with obviously high concentration of the mass compared with surrounding areas are formed by organized structures of turbulence. In this study, we extract the high concentration areas and investigate their diffusion process. For this purpose, a combination of Planar Laser Induced Fluorescence (PLIF) and Particle Image Velocimetry (PIV) techniques was employed to obtain simultaneously the two fields of the concentration of injected dye and of the velocity in a water turbulent channel flow. With focusing on a quasi-homogeneous turbulence in the channel central region, a series of PLIF and PIV images were acquired at several different downstream positions. We applied a conditional sampling technique to the PLIF images to extract the high concentration areas, or spikes, and calculated the conditional-averaged statistics of the extracted areas such as length scale, mean concentration, and turbulent diffusion coefficient. We found that the averaged length scale was constant with downstream distance from the diffusion source and was smaller than integral scale of the turbulent eddies. The spanwise distribution of the mean concentration was basically Gaussian, and the spanwise width of the spikes increased linearly with downstream distance from the diffusion source. Moreover, the turbulent diffusion coefficient was found to increase in proportion to the spanwise distance from the source. These results reveal aspects different from those of regular mass diffusion and let us conclude that the diffusion process of the spikes differs from that of regular mass diffusion.

General semi-analytical solutions to one-dimensional consolidation for unsaturated soils

This paper presents general semi-analytical solutions to Fredlund and Hasan＇s one-dimensional （1D） consolidation equations for unsaturated soils subject to different initial conditions, homogeneous boundaries and time-dependent loadings. Two variables are introduced to transform the two-coupled governing equations of pore-water and poreair pressures into an equivalent set of partial differential equations （PDEs）, which are solved with the Laplace transform method. The pore-water and pore-air pressures and settlement are obtained in the Laplace transform domMn. The Crump＇s method is used to perform inverse Laplace transform to obtain the solutions in the time domain. The present solutions are more general in practical applications and show good agreement with the previous solutions in the literature.

Direct numerical simulation study of the interaction between the polymer effect and velocity gradient tensor in decaying homogeneous isotropic turbulence

Direct numerical simulation of decaying homogeneous isotropic turbulence （DHIT） of a polymer solution is performed. In order to understand the polymer effect on turbulence or additive-turbulence interaction, we directly investigate the influence of polymers on velocity gradient tensor including vorticity and strain. By visualizing vortex tubes and sheets, we observe a remarkable inhibition of vortex structures in an intermediate-scale field and a small-scale field but not for a large scale field in DHIT with polymers. The geometric study indicates a strong relevance among the vorticity vector, rate-of-strain tensor, and polymer conformation tensor. Joint probability density functions show that the polymer effect can increase ＂strain generation resistance＂ and ＂vorticity generation resistance＂, i.e., inhibit the generation of vortex sheets and tubes, ultimately leading to turbulence inhibition effects.

An Elliptic Gradient Estimate for A Non-homogeneous Heat Equation on Complete Noncompact Manifolds

Let M be an n-dimensional complete noncompact Riemannian manifold. In this paper, we will give the elliptic gradient estimate for positive smooth solutions to the non-homogeneous heat equation(?_t-△)u(x, t) = A(x, t)when the metric evolves under the Ricci flow. As applications, we get Harnack inequalities to compare solutions at the same time.

Method of coupling 1-D unsaturated flow with 3-D saturated flow on large scale

A coupled unsaturated-saturated water flow numerical model was developed. The water flow in the unsaturated zone is considered the one-dimensional vertical flow, which changes in the horizontal direction according to the groundwater table and the atmospheric boundary conditions. The groundwater flow is treated as the three-dimensional water flow. The recharge flux to groundwater from soil water is considered the bottom flux for the numerical simulation in the unsaturated zone, and the upper flux for the groundwater simulation. It connects and unites the two separated water flow systems. The soil water equation is solved based on the assumed groundwater table.and the subsequent predicted recharge flux. Then, the groundwater equation is solved with the predicted recharge flux as the upper boundary condition. Iteration continues until the discrepancy between the assumed and calculated groundwater nodal heads have a certain accuracy. Illustrative examples with different water flow scenarios regar.ding the Dirichlet boundary condition, the Neumann boundary condition, the a.tmospheric boundary condition, and the source or sink term were calculated by the coupled model. The results are compared with those of other models, including Hydrus-lD, SWMS-2D, and FEFLOW, which demonstrate that the coupled model is effective and accurate and can significantly reduce the computational time for the large number of nodes in saturated-unsaturated water flow simulation.

Performance Optimization of Torque Converters Based on Modified 1D Flow Model

A methodology for performance optimization of torque converters is put forward based on the one-dimensional (1D) flow model. It is found that the inaccuracy of 1D flow model for predicting hydraulic performance at the low speed ratio is mainly caused by the separation phenomenon at the stator cascade which is induced by large flow impinging at the pressure side of the stator blades. A semi-empirical separation model is presented and incorporated to the original 1D flow model. It is illustrated that the improved model is able to predict the circumferential velocity components accurately, which can be applied to performance optimization. Then, the Pareto front is obtained by using the genetic algorithm (GA) in order to inspect the coupled relationship among stalling impeller torque capacity, stalling torque ratio and efficiency. The efficiency is maximized on the premise that a target stalling impeller torque capacity and torque ratio are achieved. Finally, the optimized result is verified by the computational fluid dynamics(CFD) simulation, which indicates that the maximal efficiency is increased by 0.96%.

Numerical Simulation of An Axial Flow Fan with Proper Aft Fins for Floating Wind Turbines Model Test

It is difficult to generate homogeneous wind in model test for floating wind turbines,especially when using array of axial fans.We design and compare proper fins behind the blades for an axial fan to produce anti-twist flow based on the computational fluid dynamics(CFD).The result is promising and proves that suitable designed fins can be an effective solution.

Dynamic feature analysis in bidirectional pedestrian flows

Analysis of dynamic features of pedestrian flows is one of the most exciting topics in pedestrian dynamics. This paper focuses on the effect of homogeneity and heterogeneity in three parameters of the social force model, namely desired velocity, reaction time, and body size, on the moving dynamics of bidirectional pedestrian flows in the corridors. The speed and its deviation in free flows are investigated. Simulation results show that the homogeneous higher desired speed which is less than a critical threshold, shorter reaction time or smaller body size results in higher speed of flows. The free dynamics is more sensitive to the heterogeneity in desired speed than that in reaction time or in body size. In particular, an inner lane formation is observed in normal lanes. Furthermore, the breakdown probability and the start time of breakdown are focused on. This study reveals that the sizes of homogeneous desired speed, reaction time or body size play more important roles in affecting the breakdown than the heterogeneities in these three parameters do.

HOMOGENIZATION RESULTS FOR ENZYME CATALYZED REACTIONS THROUGH POROUS MEDIA

The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distributed reactive solid obstacles,with period ε.The asymptotic behavior of the solution of such a problem is governed by a new elliptic boundary-value problem,with an extra zero-order term that captures the effect of the enzymatic reactions.

Elastoplastic homogenization of particulate composites complying with the Mohr–Coulomb criterion and undergoing isotropic loading

This work aims at determining the overall response of a two-phase elastoplastic composite to isotropic loading. The composite under investigation consists of elastic particles embedded in an elastic perfectly plastic matrix governed by the Mohr-Coulomb yield criterion and a non-associated plastic flow rule. The composite sphere assemblage model is adopted, and closed-form estimates are derived for the effective elastoplastic properties of the composite either under tensile or compressive isotropic loading. In the case when elastic particles reduce to voids, the composite in question degenerates into a porous elastoplastic material. The results obtained in the present work are of interest, in particular, for soil mechanics.

Cu^(2+)-Catalyzed Oscillatory Oxidation of Ascorbic Acid by O_2 Flow

A novel heterogeneous oscillator, the Cu2+-catalyzed oscillatory oxidation of ascorbic acid (Vitamin C) in aqueous solution by O-2 flow was reported. Both the potential oscillations on Pt-electrode corresponding to [Cu2+] and the absorbance oscillations at lambda =260 nm corresponding to [ascorbic acid] were observed. Oscillations in the completely homogeneous system were also observed. Effects of several factors on the oscillations were investigated.

2D-simulation of wet steam flow in a steam turbine with spontaneous condensation

Removal of condensates from wet steam flow in the last stages of steam turbines significantly promotes stage efficiency and prevents erosion of rotors. In this paper, homogeneous spontaneous condensation in transonic steam flow in the 2-D rotor-tip section of a stage turbine is investigated. Calculated results agree with experimental data reasonably well. On the basis of the above work, a 2-D numerical simulation of wet steam flow in adjacent root sections of a complex steam turbine stage was carded out. Computational results were analyzed and provide insights into effective removal of humidity.