Dam-Break Flows Over a Bottom Drop

The single-layer shallow-water model is used to study flows generated by dam break over a bed level discontinuity in the form of a drop from which water flows. Emphasis is given to submerged regimes in which downstream wave processes affect the upstream flow. The paper considers solutions in which the total flow energy is conserved on the drop and solutions in which the energy is lost on the drop.     

Flows formed after the passage of a discontinuous wave over a bottom drop

The solvability of the problem of the flow formed after a discontinuous wave has passed over a bottom drop is studied within the framework of the first approximation of shallow water theory. Solutions in which the total energy of the flow is either conserved or lost at the drop are considered. Stable self-similar solutions of five qualitatively different types are derived and their domains of existence are determined in the dimensionless parameter plane.     

Waves behind a Step in an Open Channel

The paper presents experimental data on flow in the vicinity of a sudden elevation of channel bottom (step). The range of external flow parameters is considered for the case where the step generates waves. A distinguishing feature of these waves is that they are formed in transition from subcritical to supercritical flow. It is shown that there is a range of external parameters in which the depth at the channel exit, the depth above the step, and the distance from the step to the first wave trough depend exclusively on flow discharge.     

Modelling of a single drop impact onto liquid film using particle method

The process of single liquid drop impact on thin liquid surface is numerically simulated with moving particle semi‐implicit method. The mathematical model involves gravity, viscosity and surface tension. The model is validated by the simulation of the experimental cases. It is found that the dynamic processes after impact are sensitive to the liquid pool depth and the initial drop velocity. In the cases that the initial drop velocity is low, the drop will be merged with the liquid pool and no big splash is seen. If the initial drop velocity is high enough, the dynamic process depends on the liquid depth. If the liquid film is very thin, a bowl‐shaped thin crown is formed immediately after the impact. The total crown subsequently expands outward and breaks into many tiny droplets. When the thickness of the liquid film increases, the direction of the liquid crown becomes normal to the surface and the crown propagates outward. It is also found that the radius of the crown is described by a square function of time: r_C = [c(t ? t₀)]^0.5. When the liquid film is thick enough, a crown and a deep cavity inside it are formed shortly after the impact. The bottom of the cavity is initially oblate and then the base grows downward to form a sharp corner and subsequently the corner moves downward. Copyright © 2004 John Wiley & Sons, Ltd.     

Numerical study of a single drop impact onto a liquid film up to the consequent formation of a crown

In this paper, the whole dynamic process of a single drop impact onto a thin liquid surface up to the consequent formation of a thin crown is numerically studied using the smoothed particle hydrodynamics (SPH) method. Especially, the gravity, artificial viscosity, and surface tension are introduced into the model. The obtained SPH numerical results are compared with experimental results. The numerical model of the SPH method is valid for simulating the dynamic process of a single drop impact onto a liquid surface. Meanwhile, it is found that the whole dynamic process mainly depends on the depth of the liquid pool and the initial velocity of the droplet.     

A Whitham–Boussinesq long-wave model for variable topography

We study the propagation of water waves in a channel of variable depth using the long-wave asymptotic regime. We use the Hamiltonian formulation of the problem in which the non-local Dirichlet–Neumann operator appears explicitly in the Hamiltonian, and propose a Hamiltonian model for bidirectional wave propagation in shallow water that involves pseudo-differential operators that simplify the variable-depth Dirichlet–Neumann operator. The model generalizes the Boussinesq system, as it includes the exact dispersion relation in the case of constant depth. Analogous models were proposed by Whitham for unidirectional wave propagation. We first present results for the normal modes and eigenfrequencies of the linearized problem. We see that variable depth introduces effects such as a steepening of the normal modes with the increase in depth variation, and a modulation of the normal mode amplitude. Numerical integration also suggests that the constant depth nonlocal Boussinesq model can capture qualitative features of the evolution obtained with higher order approximations of the Dirichlet–Neumann operator. In the case of variable depth we observe that wave-crests have variable speeds that depend on the depth. We also study the evolutions of Stokes waves initial conditions and observe certain oscillations in width of the crest and also some interesting textures and details in the evolution of wave-crests during the passage over obstacles.     

Surface waves induced by external periodic pressure in a fluid with an uneven bottom

The behavior of waves generated by periodic pressure on the free surface is considered within the linear shallow-water theory. The fluid depth is a piecewise-constant function, which implies the presence of a finite-size bottom trench or elevation. For an arbitrary shape of bottom unevenness, the solution of the problem reduces to a system of integral boundary equations. Manifestation of wave-guiding properties of bottom unevenness is illustrated by an example of an extended rectangular elevation.Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 1, pp. 70–77, January–February, 2005.     

MOTION AND DEFORMATION OF VISCOUS DROP IN STOKES FLOW NEAR RIGID WALL

A boundary integral method was developed for simulating the motion and deformation of a viscous drop in an axisymmetric ambient Stokes flow near a rigid wall and for direct calculating the stress on the wall. Numerical experiments by the method were performed for different initial stand-off distances of the drop to the wall, viscosity ratios, combined surface tension and buoyancy parameters and ambient flow parameters. Numerical results show that due to the action of ambient flow and buoyancy the drop is compressed and stretched respectively in axial and radial directions when time goes. When the ambient flow action is weaker than that of the buoyancy the drop raises and bends upward and the stress on the wall induced by drop motion decreases when time advances. When the ambient flow action is stronger than that of the buoyancy the drop descends and becomes flatter and flatter as time goes. In this case when the initial stand-off distance is large the stress on the wall increases as the drop evolutes but when the stand-off distance is small the stress on the wall decreases as a result of combined effects of ambient flow, buoyancy and the stronger wall action to the flow. The action of the stress on the wall induced by drop motion is restricted in an area near the symmetric axis, which increases when the initial stand-off distance increases. When the initial stand-off distance increases the stress induced by drop motion decreases substantially. The surface tension effects resist the deformation and smooth the profile of the drop surfaces. The drop viscosity will reduce the deformation and migration of the drop.     

A numerical method for the determination of weakly non‐hydrostatic non‐linear free surface wave propagation

A numerical method is described that may be used to determine the propagation characteristics of weakly non‐hydrostatic non‐linear free surface waves over a general, bottom topography. In shallow water of constant undisturbed depth, such waves are equivalent to the familiar cnoidal waves characterized by sharp crests and relatively flat troughs. For a certain range of parameters, these propagate without change of form by virtue of the weakly non‐hydrostatic balance in the vertical momentum equation. Effectively, this counters the tendency for the non‐linearity in a purely hydrostatic theory to lead to a continuously deforming surface wave profile. The realistic representation furnished by cnoidal wave theory of free surface waves in the shallow near‐shore zone has led to its utilization in evaluating their propagation characteristics. Nonetheless, the classic analytical theory is inapplicable to the case of wave propagation over a sloping beach or off‐shore sand bar topography. Under these conditions, a local change in form of the surface wave profile is anticipated before the waves break and knowing this is required in order to evaluate fully the propagation process. The efficacy of the numerical method is first demonstrated by comparing the solution for water of constant depth with the evaluation of the analytical solution expressed in terms of the Jacobian elliptic function cn. The general method described in the paper is then illustrated by experiments to determine the change in profile of weakly non‐hydrostatic non‐linear surface waves propagating over bed forms representative of those found in shallow coastal seas. Copyright © 2001 John Wiley & Sons, Ltd.     

Higher order Boussinesq-type equations for water waves on uneven bottom

Higher order Boussinesq-type equations for wave propagation over variable bathymetry were derived. The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain. The free surface velocities and the bottom velocities were connected by the exact solution of the Laplace equation. Taking the velocities on half relative water depth as the fundamental unknowns, terms relating to the gradient of the water depth were retained in the inverse series expansion of the exact solution, with which the problem was closed. With enhancements of the finite order Taylor expansion for the velocity field, the application range of the present model was extended to the slope bottom which is not so mild. For linear properties, some validation computations of linear shoaling and Booij' s tests were carried out. The problems of wave-current interactions were also studied numerically to test the performance of the enhanced Boussinesq equations associated with the effect of currents. All these computational results confirm perfectly to the theoretical solution as well as other numerical solutions of the full potential problem available.     

近岸非平整海底上耗散动力系统的广义波作用量守恒方程

为刻划近岸波-流-海底相互作用耗散动力系统的多种复杂作用机制，着眼于波浪对近岸大尺度变化环境流作用和考虑多变海底地形(可典型地刻划为由慢变水深和快变水深构成)的影响，由基于黏性流体Navie-Stokes方程的平均流方程，建立了近岸耗散动力系统的广义波作用量守恒方程，从中提出垂向速度波作用量和耗散波作用量这两种新概念，使得它们和经典的波作用量相互间达成了一种互补、协调而又主次分明的更为广泛的守恒形式．从而把波作用量这一经典概念从理想的平均流守恒系统引申到实际的平均流耗散系统(即广义守恒系统)中去，为解释沿岸过程和应用于近海、海岸工程提供了一个理论基础．     

QUASICONTINUUM SIMULATION OF NANOINDENTATION OF NICKEL FILM

A large-scale atom simulation of nanoindentation into a thin nickel film using thequasicontinuum method was performed. The initial stages of the plasticity deformation of nickelwere studied. Several useful results were obtained as follows: (1)The response of the load versusindentation depth—on the load versus indentation depth curve, besides the straight parts cor-responding to the elastic property of nickel, the sudden drop of the load occurred several times;(2) The phenomena of dislocation nucleation—the dislocation nucleation took place when theload descended, which makes it clear that dislocation nucleation causes the drop of the load;(3)The mechanism of the dislocation emission—the Peierls-Nabarro dislocation model and a pow-erful criterion were used to analyze the dislocation emission. And the computational value was ingood agreement with the predict value; (4) The density of geometrically necessary dislocations.A simple model was used to obtain the density of geometrically necessary dislocations beneaththe indenter. Furthermore, the influence of the boundary conditions on the simulation results wasdiscussed.     

镍单晶薄膜纳米压痕的准连续介质模拟

用准连续介质方法模拟了大规模原子的镍薄膜在纳米压痕下发生初始塑性变形的行为.主要得到了:(1)载荷-位移响应.在载荷位移曲线上除了反应晶体弹性性质的直线外还有数次的载荷突然下降过程.(2)位错形核现象.与载荷-位移曲线上的载荷突然下降相对应的在受压的晶体上发现了位错形核现象,说明载荷的下降是因为位错形核引起的.(3)位错的发射机制.用Peierls-Nabarro位错模型以及能量法分析了位错的发射机制,理论值与计算值吻合较好.(4)几何必需位错密度.用一个简单的模型计算了几何必须位错密度.此外还考虑了边界条件对模拟结果的影响.     

Multi-objective optimization of a dimpled channel for heat transfer augmentation

Staggered arrays of dimples printed on opposite surfaces of a cooling channel is formulated numerically and optimized with hybrid multi-objective evolutionary algorithm and Pareto optimal front. As Pareto optimal front produces a set of optimal solutions, the trends of objective functions with design variables are predicted by hybrid multi-objective evolutionary algorithm. The problem is defined by three non-dimensional geometric design variables composed of dimpled channel height, dimple print diameter, dimple spacing, and dimple depth, to maximize heat transfer rate compromising with pressure drop. Twenty designs generated by Latin hypercube sampling were evaluated by Reynolds-averaged Navier–Stokes solver and the evaluated objectives were used to construct Pareto optimal front through hybrid multi-objective evolutionary algorithm. The optimum designs were grouped by k-means clustering technique and some of the clustered points were evaluated by flow analysis. With increase in dimple depth, heat transfer rate increases and at the same time pressure drop also increases, while opposite behavior is obtained for the dimple spacing. The heat transfer performance is related to the vertical motion of the flow and the reattachment length in the dimple.     

SIMILARITY LAWS OF HYPERVELOCITY PENETRATION EFFECTS OF CONCRETE1)

为了研究混凝土超高速侵彻效应的相似规律,总结相似关系基本理论并开展1.4~3.9 km/s 的混凝土侵彻实验,综合本文实验和相关文献实验结果确定关键相似准数并得到归一化侵彻深度的变化规律。结果表明,归一化侵彻深度主要取决于Johnson 数、弹靶密度比和弹体长径比,弹靶强度比和弹头形状系数等因素影响不大;归一化侵彻深度随归一化撞击速度增加而先增后减;当撞击速度接近混凝土纵波声速时,存在以侵彻深度突降为主要现象的“跨声速效应”。     

Penetration length and diameter development of vortex rings generated by impacting water drops

The formation of water drops underneath nozzles was studied numerically to provide the basis for repeatable experimental drop formation. The drops detached from the nozzle and impacted on a free water surface forming vortex rings. Experimental results obtained through kinematographic studies of the penetration and growth of these vortex rings are presented. Variations of the penetration depth were measured, depending on the nozzle height above the water surface where the drops were formed. The experiments revealed that it is the state of oscillation at impact that defines the penetration length. Interesting variations of the vortex ring diameter with time were recorded. A good overall understanding of the behavior of the diameter variation was obtained when it was plotted as a function of the penetration depth.     

On the discharge characteristic at the dam site after dam break

A review of the information available in the literature is given, and new experimental data on the depth and discharge at the dam site after a total and a partial dam break are presented. It is shown that in the case of a partial dam break with the formation of a rectangular breach, the specific discharge per unit width of the breach is higher than the specific discharge in the case of a total dam break with the same excess initial energy in the headwater. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 5, pp. 77–87, September–October, 2006.     

Collision of water drop on water

A series of experiments are performed to study the collision of a water drop with various impact velocities, ranged from 0 to 600 cm/s, onto a water surface. Three kinds of phenomena have been recorded. Two of them named “penetration” and “cleavage”, were observed for low impact velocity (up to 100 cm/s). Their common characteristics are that no obvious disturbances on the surface were observed during the colliding process. Namely no splashing jets nor obvious crater were observed. By penetration we mean that a drop fallen into water becomes a ring, which penetrates the water smoothly with a velocity of several centimeters per second. During the penetrating process no obvious change of its configuration was observed. The falling height corresponding to penetration is proportional to volume of the original drop. Some periodicity of the falling heights (corresponding to penetration) was revealed. The phenomenon named “cleavage” occurs when the impact velocity is other than that corresponding to penetration, then the drop cleaves into an “inverted cauliflower” after falling below the surface of water. It almost does not decend. By diffusing and slowly expanding it vanishes in the vessel water several minutes after. These two kinds of phenomena, as we know, have not been reported before. As the impact velocity approaches or exceeds 100 cm/s, the third kind of phenomena, the splash, appears. The diameter and depth of the crater occuring in the case of splash, together with the time for the crater to reach its maximum size, and the time for the rebounding column to begin to rise are given as functions of the falling height of the drop.     

Modelling sediment transport over partially non‐erodible bottoms

In‐depth‐averaged and cross‐section‐averaged morphodynamic models, based on explicit time integration, it may happen that the computed bed level becomes lower than the top level of a non‐erodible layer (e.g. concrete, bedrock or armoured layer). This is a standard pitfall, which has been addressed in different ways. In this paper, we present an original approach for avoiding computation of non‐physical bed levels, using an iterative procedure to correct the outward sediment fluxes. The procedure is shown to be computationally efficient while it achieves a high accuracy in terms of mass conservation. We compare our original approach with the existing Struiksma's method and with a reformulation of the problem in terms of mathematical optimization of a linear or nonlinear objective function under linear constraints. The new procedure has been incorporated into an existing finite volume morphodynamic model. It has been validated with several 1D benchmarks leading to configurations with sediment transport over non‐erodible bottom. The computation time has been verified not to increase by more than 15% compared with runs without non‐erodible bottom. Copyright © 2011 John Wiley & Sons, Ltd.     

Experimental study of the effect of friction phenomena on actual and calculated inventory in a small-scale CFB riser

Accurate information concerning riser inventory in a fluidized bed is required in some applications such as the calcium looping process, because it is related to the CO₂ capture efficiency of the system. In a circulating fluidized bed (CFB), the riser inventory is normally calculated from the riser pressure drop; however, the friction and the acceleration phenomena may have a significant influence on the total riser pressure drop. Therefore, deviation may occur in the calculation from the actual mass. For this reason the magnitude of the friction and the acceleration pressure drop in the entire riser is studied in small-scale risers. Two series of studies were performed: the first one in a scaled cold model riser of the 10 kW_th facility, and the second one in the 10 kW_th fluidized bed riser under process conditions. The velocities were chosen to comply with the fluidization regimes suitable for the calcium looping process, namely, the turbulent and the fast. In cold-model experiments in a low-velocity turbulent fluidization regime, the actual weight (static pressure drop) of the particles is observed more than the weight calculated from a recorded pressure drop. This phenomenon is also repeated in pilot plant conditions. In the cold-model setup, the friction and acceleration pressure drop became apparent in the fast fluidization regime, and increased as the gas velocity rose. Within calcium looping conditions in the pilot plant operation, the static pressure drop was observed more than the recorded pressure drop. Therefore, as a conservative approach, the influence of friction pressure drop may be neglected while calculating the solid inventory of the riser. The concept of transit inventory is introduced as a fraction of total inventory, which lies in freefall zones of the CFB system. This fraction increases as gas velocity rises.