Entrainment and condensation effects in the upward acceleration of a liquid column

The instability-governed entrainment rate of the lower surface of a subcooled water column accelerated upwards by an expanding steam mass is measured. It is found that the entrainment rate is approximately proportional to the fourth root of the acceleration. This would be the case if the characteristic length scale in the late stages of Taylor instability were governed by linear instability theory. In addition to the linear displacement measurements, the steam pressure in the lower driver section was monitored as a function of time. Estimates of the concentration, radius and age distribution of the entrained droplet population were made by modeling the bubble-and-spike breakup into discrete droplets. This allows the steam condensation rate, and hence the steam pressure, at each instant of time to be computed. This is compared with the observed steam pressure history. Reasonable agreement is found. One can thus estimate the reduction in work potential in the case of a steam explosion in the lower plenum of a pressurized-water nuclear reactor.     

Parameterization of the in-water motions of falling cylinders using high-speed video

A methodology to observe the motions of large cylinders falling freely at large (~10⁶) Reynolds numbers using a stereometric, high-speed video technique is presented. Parameter variation in length, weight, center of mass, and nose shape combined with changes in release height and initial inclination angle were used to estimate the influence of net drag forces on six cylinder bodies. Cylinders with coincident centers of volume and mass typically assumed body orientations with the major axis aligned normal to the path of descent indicating that buoyancy forces and turbulent drag balanced the inertia of the body and displaced water. Displacement of the center of mass resulted in more vertical orientations and more complex motions. Abrupt changes in position, orientation, and velocity were also observed when air-dropped cylinders separated from a trapped cloud of bubbles signifying the onset of less predictable behaviors.     

The effect of liquid viscosity on mixing in falling films

The effect of liquid viscosity on mixing in falling liquid films has been investigated using a Macropore as a means of simulating conditions in a packed column.-Mass transfer coefficients and transfer unit heights have been calculated for the absorption of stagnant carbon dioxide at atmospheric pressure and 25° C into aqueous glycerol for a range of liquid rates and glycerol concentrations, and the values compared with those from Penetration theory correlations.-Deviations from expected behaviour have been observed, notably that the exponent on the overall mass transfer coefficient with respect to film Reynolds number is significantly greater than the value of one-third predicted from the Higbie model.-It has been shown that mixing at the discontinuities is more than 75% complete for pure water but that this mixing factor decreases with increasing viscosity.     

Numerical simulation of blast wave interaction with structure columns

Accurate estimation of blast loads on structures is essential for reliable predictions of structural response and damage. Current practice in blast effect analysis and design estimates blast loads primarily based on empirical formulae obtained from field blast tests. Due to the limited availability of test data, those empirical formulae are usually applicable to the case that the reflection surface of the structure is big enough so that no wave diffraction around the structure exists. They will overestimate the blast loads on structure columns without infill walls around them, which are very common in the modern buildings, especially for the ground floor columns. For a standalone column, the initial reflected pressure may be quickly relieved at the edge of the column, and the column will be engulfed with the blast wave due to diffraction. Therefore, the interaction between the blast wave and structure is important for such columns. The blast loads on such columns will be different from those obtained in field blasting tests on walls. There is no method in the open literature to estimate blast loads on standalone columns. In the present study, interactions between blast waves and structure columns are simulated using AUTODYN 3D. The influence of the scaled distance of the blast, column stiffness, ratio of the supported mass to the column mass, and column dimension and geometry, on the blast wave–column interaction is investigated. Based on the numerical simulation results, some formulae are proposed to estimate the blast pressure, impulse, and the reflected pressure time history on standalone structure columns.      

A solution for the vertical variation of stress,rather than velocity,in a three-dimensional circulation model

A simple technique is presented that allows a numerical solution to be sought for the vertical variation of shear stress as a substitute for the vertical variation of velocity in a three-dimensional hydrodynamic model. In its most general form the direct stress solution (DSS) method depends only upon the validity of an eddy viscosity relation between the shear stress and the vertical gradient of velocity. The rationale for preferring a numerical solution for shear stress to one for velocity is that shear stress tends to vary more slowly over the vertical than velocity, particularly near boundaries. Consequently, a numerical solution can be obtained much more efficiently for shear stress than for velocity. When needed, the velocity profile can be recovered from the stress profile by solving a one-dimensional integral equation over the vertical. For most practical problems this equation can be solved in closed form. Comparisons are presented between the DSS technique, the standard velocity solution technique and analytical solutions for wind-driven circulation in an unstratified, closed, rectangular channel governed by the linear equations of motion. In no case was the computational effort required by the velocity solution competitive with the DSS when a physically realistic boundary layer was included. The DSS technique should be particularly beneficial in numerical models of relatively shallow water bodies in which the bottom and surface boundary layers occupy a significant portion of the water column.     

Nonisothermal multiphase flow of brine and gas through saline media

We propose a general formulation for nonisothermal multiphase flow of brine and gas through saline media. The balance equations include mass balance (three species), equilibrium of stresses and energy balance (total internal energy). Salt, water and air mass balance equations are established. The balance of salt allows the establishment of the equation for porosity evolution due to solid skeleton deformation, dissolution/precipitation of salt and migration of brine inclusions. Water and air mass balance equations are also obtained. Two equations are required for water: total water in the medium and water present in solid phase brine inclusions. The mechanical problem is formulated through the equation of stress equilibrium. Finally, the balance of internal energy is established assuming thermal equilibrium between phases. Some general aspects of the constitutive theory are also presented.     

Modeling of simultaneous heat and mass transfer processes in ammonia–water absorption systems from general correlations

This paper presents a general differential mathematical model to analyze the simultaneous heat and mass transfer processes that occur in different components of an ammonia–water absorption system: absorber, desorber, rectifier, distillation column, condenser and evaporator. Heat and mass transfer equations are considered, taking into account the heat and mass transfer resistances in the liquid and vapour phases. The model considers the different regions: vapour phase, liquid phase and an external heating or cooling medium. A finite difference numerical method has been considered to solve the resulting set of nonlinear differential equations and an iterative algorithm is proposed for its solution. A map of possible solutions of the mass transferred composition z is presented when varying the interface temperature, which enables to establish a robust implementation code. The analysis is focused on the processes presented in ammonia–water absorption systems. The model is applied to analyze the ammonia purification process in an adiabatic packed rectification column and the numerical results show good agreement with experimental data.     

Effects of dry density and thickness of sandy soil on impact response due to rockfall

Sand cushions against impact force are widely used for rockfall prevention covers. The objective of this paper is to investigate the effects of the dry density and thickness of a sand cushion on an impact response due to a falling weight likened to a rockfall. A series of laboratory experiments for a decomposed granite soil was executed in the combination of the mass and drop height of the weight. As a result, the impact pressure applied to the soil surface increases with the dry density, but it does not depend on the thickness of the soil. The earth pressure at the bottom of the mold increases with the dry density, and it decreases with the thickness of the soil. Therefore, the transmissibility of the impact pressure decreases rapidly with the thickness of the soil.     

A two-fluid model for critical vapour-liquid flow

One-dimensional two-fluid equations are used to calculate the mass flux of initially saturated or subcooled water discharging from a pipe in critical flow. The model allows in a general way for thermal non-equilibrium between the liquid and vapour bubbles, and for interphase relative motion. The theory is shown to be in good agreement with the measured critical flow-rates of pressurised water over a wide pressure range for a single choice of parameters characterising (i) the density of nucleation sites in the liquid, (ii) the liquid superheat required to cause bubble nucleation. Predictions are made of the critical mass flux of initially saturated water in pipes of the range of sizes of interest in water-reactor blowdown safety analysis. Results indicate that for pipes up to ten diameters in length flows will be significantly higher than values obtained from conventional homogeneous thermal equilibrium flow theory.     

On the theory of the Cherepnov water lifter

An approximate analysis is presented of the Cherepnov water lifter, considered as a self-oscillatory system which performs relaxation oscillations at the expense of the energy of falling water. It is noted that, in contrast with the hydraulic ram, the water inertia is not essential to the operation of the water lifter.     

动能侵彻弹体的质量侵蚀模型分析

通过对高速侵彻弹体的质量侵蚀实验现象进行分析,建立了质量侵蚀的工程理论模型,可对动能侵彻弹体头部侵蚀后的头形和质量侵蚀进行预期. 讨论弹体质量侵蚀的主要影响因素,认为弹体动能(或质量和速度)以及混凝土骨料硬度对弹体的质量侵蚀有显著影响,给出了更一般化的弹体质量侵蚀与撞击函数$I$的关系. 通过图形分析明确弹体的质量侵蚀主要发生于头部,并且侵蚀后的弹头仍接近尖卵形,可以通过头形变化预期弹体的质量损失.      

Detonability of fuel-oxygen and fuel-air mixtures

An analysis of theoretical models and experimental investigations of the detonability of unconfined detonation in uniform gaseous mixtures shows a disparity in results. The present study is limited to propane, acetylene and methane diluted with oxygen or air in variable proportions and initial pressures at ambient temperature conditions. Because of the disparity in results, a simple and general formulation of critical initiation energy for gaseous detonations has been investigated. The problem has been formulated using the conservation equation of total energy enclosed by the shock. From this, a simple form for the critical energy has been deduced. This approach leads to a good simulation in uniform mixtures, regardless of initiation conditions. Some applications are presented in this paper. A new experimental study on the detonability of methane/oxygen mixtures diluted with propane and/or nitrogen is reported. The gaseous mixtures are confined in a cylindrical vessel. The initial conditions are various equivalence ratio and pressure under room temperature. In the case of methane/oxygen mixtures, the predetonation radius varies directly with the cell width. The constant ratio is in the order of 18, slightly different from the classical relation R _c= 20λ. For propane the slope variation of the critical energy versus initial pressure depends on the dilution. We have compared the critical energy obtained by several authors with the theoretical values. Fuel ratio and initial pressure are the chosen parameters. These comparisons show that the formulation allows for the prediction of the critical energy of detonation of uniform mixtures with a good estimation range. The correlation between the different geometries has been deduced and a test has been conducted as well in the case of stoichiometric methane/oxygen and acetylene/oxygen mixtures versus initial pressure for a cylindrical detonation. Received 9 January 1996 / Accepted 24 January 1997     

Mass and heat transfer during solid sphere dissolution in a non-uniform fluid flow

We studied a nonisothermal dissolution of a solvable solid spherical particle in an axisymmetric non-uniform fluid flow when the concentration level of the solute in the solvent is finite (finite dilution of solute approximation). It is shown that simultaneous heat and mass transfer during solid sphere dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with a parabolic velocity profile can be described by a system of generalized equations of convective diffusion and energy. Solutions of diffusion and energy equations are obtained in an exact analytical form. Using a general solution the asymptotic solutions for heat and mass transfer problem during spherical solid particle dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with parabolic velocity profile are derived. Theoretical results are in compliance with the available experimental data on falling urea particles dissolution in water and for solid sphere dissolution in a shear flow.     

Condensation induced water hammer: Numerical prediction

Contact of steam and subcooled water in a pipe or a pressurized vessel leads to intensive condensation accompanied by a pressure drop in the volume of condensing steam and an acceleration of the surrounding water mass towards the steam volume, which can result in a severe water hammer and plant damage. This phenomenon is known as the condensation induced water hammer (CIWH). A one-fluid model is developed for the prediction of pressure surges during CIWH. It is shown that the reliable prediction of pressure surges strongly depends on the calculation of the condensation rate, transient friction and the water column–steam interface tracking. Due to the lack of the CIWH condensation models, a new approach is derived. The one-fluid model predictions of pressure surges are compared with available measured data from a CIWH experimental facility and acceptable agreements are obtained. In addition, the ability of the developed model to simulate the water cannon event, which takes place during the steam drainage into the pool of subcooled water, is demonstrated. Experimentally observed considerable scattering of test data under the same conditions is related to the condensation rate and its dependence on the entrained droplets–steam interfacial area concentration in the vicinity of the water column head.     

Modeling on mass abrasion of kinetic energy penetrator

An engineering model on mass abrasion of kinetic energy penetrator is presented to predict the nose shape and mass loss of the residual projectile after high-speed penetration into concrete. The experimental analysis indicates that the kinetic energy of penetrator (i.e., mass and velocity of projectile) and the hardness of aggregate of concrete significantly affect the mass abrasion of projectile. A theoretical upper limit exists for the mass loss. More general relationship between mass loss and impact function I of projectile is constructed. Graphical discussion declares that the most mass loss occurs on the nose of the projectile and the eroding nose approaches to an ogival shape with a smaller value of caliber-radius-head (CRH). A relative rate of mass abrasion on ogive-nose is further defined and analyzed. The mass loss from abrasion on kinetic energy (KE) penetrator may be evaluated through the variation of nose shape.     

Simulation of viscous water column collapse using adapting hierarchical grids

An adaptive hierarchical grid‐based method for predicting complex free surface flows is used to simulate collapse of a water column. Adapting quadtree grids are combined with a high‐resolution interface‐capturing approach and pressure‐based coupling of the Navier–Stokes equations. The Navier–Stokes flow solution scheme is verified for simulation of flow in a lid‐driven cavity at Re=1000. Two approaches to the coupling of the Navier–Stokes equations are investigated as are alternative face velocity and hanging node interpolations. Collapse of a water column as well as collapse of a water column and its subsequent interaction with an obstacle are simulated. The calculations are made on uniform and adapting quadtree grids, and the accuracy of the quadtree calculations is shown to be the same as those made on the equivalent uniform grids. Results are in excellent agreement with experimental and other numerical data. A sharp interface is maintained at the free surface. The new adapting quadtree‐based method achieves a considerable saving in the size of the computational grid and CPU time in comparison with calculations made on equivalent uniform grids. Copyright © 2005 John Wiley & Sons, Ltd.     

Coupled thermo-hygro-mechanical damage model for concrete subjected to high temperatures

Based on the theory of mixtures, a coupled thermo-hygro-mechanical (THM) damage model for concrete subjected to high temperatures is presented in this paper. Concrete is considered as a mixture composed of solid skeletons, liquid water, water vapor, dry air, and dissolved air. The macroscopic balance equations of the model consist of the mass conservation equations of each component and the momentum and energy conservation equations of the whole medium mixture. The state equations and the constitutive model used in the model are given. Four final governing equations are given in terms of four primary variables, i.e., the displacement components of soil skeletons, the gas pressure, the capillary pressure, and the temperature. The processes involved in the coupled model include evaporation, dehydration, heat and mass transfer, etc. Through the process of deformation failure and the energy properties, the mechanics damage evolution equations are established based on the principle of conversation of energy and the Lemaitre equivalent strain assumption. Then, the influence of thermal damage on the mechanical property is considered.     

Modeling liquefaction of water saturated granular material under undrained cyclic shearing

The tendency of particles in a water-saturated granular mass to re-arrange into a denser state during cyclic shearing under pressure results in an increase in pore water pressure. The increase in the pore water pressure causes a reduction in the inner particle contact forces, and in turn easier re-arrangement of the particles. Eventually, the material loses its shear strength, partially or almost completely. In this paper, a general three-dimensional continuum mechanics model is presented for the deformation of granular materials. A physically based model is also presented for characterization of liquefaction of the water saturated granular material under undrained cyclic shearing. The model incorporates the fabric of the granular mass, which develops as the frictional granular mass is deformed in shear. It includes the coupling between shearing and excess pore water pressure. The model parameters are estimated, based on the results of cyclic shearing experiments on large hollow cylindrical samples of silica sand. Basically, the calculation results utilizing this model can embody liquefaction phenomena of the water saturated granular material under undrained cyclic shearing.     

Method and apparatus for on-line estimation of soil parameters during excavation

Time-varying forces from soil–machine interactions cause stresses in the components of earthmoving machinery, which may cause damage to the machine. It is not always possible to know all the characteristics of a soil sample prior to excavation; however, by estimating necessary soil parameters, it is possible to predict the soil–machine interaction forces in a practical manner. This article presents the development of a simple apparatus and method for estimating the soil parameters from the cutting force measured by the novel bench-scale excavating tool, validation of the soil model, and comparison with other available techniques. The apparatus used to collect data of soil forces on a tool consists of an instrumented crank-slider mechanism equipped with a thin plate to fragment the soil, which is contained in a sample box. Using the Mohr-Coulomb earth pressure model to predict failure force during the interaction, two methods are used to minimize the error between the predicted and measured failure force, that allows to estimate soil parameters: First, the Newton–Raphson Method (NRM) is used to minimize the error, which allows estimation of two soil parameters (interface friction angles) on non-cohesive soil samples. Additionally, a new estimation scheme based on the NRM is presented, that uses an auxiliary equation, and allows estimation of up to three soil parameters, including interface friction angles and cohesion. Comparing the results obtained from the presented apparatus, it is confirmed that the friction angles are successfully estimated for two non-cohesive particulate materials. Additionally, it is shown that the new scheme demonstrates smaller error in estimating soil parameters for cohesive and non-cohesive soil samples than previously reported methods. The parameter estimation method is subsequently applied to determine the properties of highly cohesive oil sand, and delivers promising results.