Seiches in a channel with a sharp variation in the bottom relief

A mathematical model of seiches is developed for the case of sharp bottom elevation or depression. An effective high-precision numerical and analytical method is applied to determine the natural frequencies and shapes of the lower modes of oscillations. New important hydrodynamic effects of the bottom relief are revealed. The main features of standing waves in a narrow vessel in the presence of sharp bottom elevation are confirmed by laboratory experiments.     

Analytical and numerical studies for Seiches in a closed basin with bottom friction

A standing wave oscillation in a closed basin, known as a seiche, could cause destruction when its period matches the period of another wave generated by external forces such as wind, quakes, or abrupt changes in atmospheric pressure. It is due to the resonance phenomena that allow waves to have higher amplitude and greater energy, resulting in damages around the area. One condition that might restrict the resonance from occurring is when the bottom friction is present. Therefore, a modified mathematical model based on the shallow water equations will be used in this paper to investigate resonance phenomena in closed basins and to analyze the effects of bottom friction on the phenomena. The study will be conducted for several closed basin shapes. The model will be solved analytically and numerically in order to determine the natural resonant period of the basin, which is the period that can generate a resonance. The computational scheme proposed to solve the model is developed using the staggered grid finite volume method. The numerical scheme will be validated by comparing its results with the analytical solutions. As a result of the comparison, a rather excellent compatibility between the two results is achieved. Furthermore, the impacts that the friction coefficient has on the resonance phenomena are evaluated. It is observed that in the prevention of resonances, the bottom friction provides the best performance in the rectangular type while functioning the least efficient in the triangular basin. In addition, non-linearity effect as one of other factors that provide wave restriction is also considered and studied to compare its effect with the bottom friction effect on preventing resonance.     

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.     

Onset of Convection in a Porous Rectangle with Buoyancy Along an Open Sidewall

The onset of thermal convection in a two-dimensional porous box is investigated analytically. One of the two lateral boundaries is in contact with a hydrostatic reservoir, where the saturating fluid can flow freely in and out. This open boundary is thermally insulating, but with the buoyancy of the fluid taken into account. For the second lateral wall, we study five different options for the boundary conditions. This leads to five different eigenvalue problems for the onset of convection. These five solutions are compared with the known solutions where the buoyancy along open sidewalls is neglected (Tyvand 2002).     

Supercritical Flow Over a Sill in an Open Channel

Experimental data on typical profiles of free surface and channel bottom pressure for a supercritical flow over a sill are reported. This flow is shown to have, along with the known critical depth, two other characteristic depths, one of which is at the channel exit to the atmosphere and the other determines conditions under which the disturbances propagate well upstream of the sill. The experimental data are compared with calculation results based on a mathematical model that incorporates turbulent mixing upon wave breaking.     

Transcritical Flow over a Ramp in an Open Channel

Steady free-surface flows over an elongated obstacle located on the channel bottom are studied theoretically and experimentally. For determining the free-surface shape and the main flow parameters, the first and second shallow-water approximations are used. In the second approximation, a solution describing a smooth transition from the subcritical to superctitical flow is found. A mathematical model of the hydraulic jump behind the ramp is constructed. The results of the mathematical modeling are compared with experimental data.     

Stability of Flow with Viscous Dissipation in a Horizontal Porous Layer with an Open Boundary Having a Prescribed Temperature Gradient

A buoyancy-induced stationary flow with viscous dissipation in a horizontal porous layer is investigated. The lower boundary surface is impermeable and subject to a uniform heat flux. The upper open boundary has a prescribed, linearly varying, temperature distribution. The buoyancy-induced basic velocity profile is parallel and non-uniform. The linear stability of this basic solution is analysed numerically by solving the disturbance equations for oblique rolls arbitrarily oriented with respect to the basic velocity field. The onset conditions of thermal instability are governed by the Rayleigh number associated with the prescribed wall heat flux at the lower boundary, by the horizontal Rayleigh number associated with the imposed temperature gradient on the upper open boundary, and by the Gebhart number associated with the effect of viscous dissipation. The critical value of the Rayleigh number for the onset of the thermal instability is evaluated as a function of the horizontal Rayleigh number and of the Gebhart number. It is shown that the longitudinal rolls, having axis parallel to the basic velocity, are the most unstable in all the cases examined. Moreover, the imposed horizontal temperature gradient tends to stabilise the basic flow, while the viscous dissipation turns out to have a destabilising effect.     

Entrance flow of a bingham fluid in a tube

The numerical solution of the entrance flow in a tube has been obtained for a Bingham fluid. The numerical procedure used is that of Patankar and Spalding [1]. The accuracy of the numerical results is demonstrated by comparing the fully-developed velocity profiles with analytical exact solutions. The results of the entrance flow in a tube for the case of a zero yield stress are compared with the entrance flow solution for a Newtonian fluid. Detailed results are presented for a wide range of yield numbers (=τ _y D/ūμ).     

Entrance flow of a yield-power law fluid

In the present work we have obtained the numerical solution of the momentum equation for a Yield-Pseudoplastic power-law fluid flowing in the entrance region of a tube. The accuracy of the numerical results is checked by comparing the asymptotic values of friction coefficients and velocity profiles with the corresponding results from the analytical solutions for the fully-developed region. The results of the entrance flow solution for the power-law exponent equal to unity (Bingham fluid) are also in agreement with the numerical solution for a Bingham fluid. Detailed results are presented for wide ranges of yield numbers and power law exponents.

Nomenclature

Nomenclature a constant - D diameter - F dimensionless pressure gradient in (4.3) - f _x friction factor in (5.1) - f _app total friction factor in (5.2) - K entrance pressure drop coefficient - n power law exponent - p pressure - r radial co-ordinate - R radius of a tube - Re Reynolds number (5.3) - s rate of shear, u/r - u axial velocity - average velocity - v velocity in radius direction - x axial co-ordinate - y normal co-ordinate - Y yield number in (4.4) - z dimensionless axial distance =(x/D)/Re - z ₁ 1/z Greek Symbols plug flow radius in (4.6) - _eff effective viscosity - density - shear stress - _y yield stress - dimensionless stream function     

Basin boundaries with nested structure in a shallow arch oscillator

The basin boundaries with nested structure are investigated in a shallow arch oscillator. Basin organization is complex yet systematic and it is governed by the ordering of heteroclinic and homoclinic connections of regular saddles. The Wada properties are verified for eight basin boundaries, where five basin boundaries are totally Wada basin boundaries for a given set of parameters. The organization of nested basin boundaries is governed by the order of saddle connections. The term “Wada number” is introduced to describe the nested structure. The partially Wada basin boundaries are investigated by the erodent cells and the remnant cells.     

Entrance flow in eccentric annular ducts

A control-volume-based solution of the complete set of Navier-Stokes equations for the laminar, three-dimensional developing flow in straight, eccentric, cylindrical annular ducts is described. Numerical results for velocity and pressure development, pressure defect and entrance lengths are presented for a wide range of duct parameters, i.e. relative eccentricity ? and radius ratio γ. The present results match very well with earlier numerical solutions for the limiting cases of developing flow in concentric ducts and fully developed flow in eccentric ducts. Comparison with earlier approximate results for developing flow in eccentric ducts indicates that the approximate model predicts the velocity and pressure development with an error of about 10%. However, the development length predicted by the approximate model is grossly in error. The pressure defect and development length in eccentric ducts are very high compared with their counterparts in concentric ducts. The pressure defect, development length and maximum velocity increase with the radius ratio for eccentric ducts, while the reverse is true for concentric ducts. Also, the apparent friction factor decreases as the eccentricity increases.     

Triple-Diffusive Mixed Convection in a Porous Open Cavity

The triple-diffusive mixed convection heat and mass transfer of a mixture is analyzed in an enclosure filled with a Darcy porous medium. The mass transfer buoyancy effects due to concentration gradients of the dispersed components (pollutant components) are taken into account using the Boussinesq approximation model. The governing equations are transformed into a non-dimensional form, and six groups of non-dimensional parameters, including Darcy–Rayleigh number, Peclet number, two Lewis numbers for pollutant components 1 and 2 and two buoyancy ratio parameters for pollutant components 1 and 2, are introduced. The governing equations are numerically solved for various combinations of non-dimensional parameters using the finite element method. The effect of each group of non-dimensional parameters on the pollutant distribution and the heat transfer in the cavity is discussed. The results indicate that the presence of one pollutant component can significantly affect the pollutant distribution of the other component. When the Lewis number of a pollutant component is small, the increase in the bouncy ratio parameter of the proposed component always increases the Nusselt and Sherwood numbers in the cavity.     

开式热沉内冷刀具的设计及其导热性能分析

车削加工温度对工件的表面加工质量和刀具的使用寿命具有重要影响. 设计了一种开式热沉内冷刀具,计算了在实际加工工艺参数下刀具受到的切削力和前刀面上的热流密度,分析了刀具的结构强度;建立了刀具热-流-固耦合温度场模型,探讨了热稳态条件下刀具的温度场分布,以及刀片冷却液流道内热沉数量对刀具导热性能的影响规律,比较了在相同热源条件下开式热沉内冷刀具与其他内冷刀具的导热性能. 结果表明:对于刀片材料为硬质合金YT5的刀具,在热流密度为10 W/mm2的条件下,内置6个热沉的设计方案可获得最佳冷却效果,刀具的最高切削温度控制为187.1 ℃;与其他内冷刀具相比,开式热沉内冷刀具的最高切削温度降低了12.1 ℃.      

Numerical Investigation of Thermally Developing Non-Darcy Forced Convection in a Porous Circular Duct with Asymmetric Entrance Temperature Under LTNE Condition

Transport in Porous Media - This paper numerically investigates the heat transfer performance of thermally developing non-Darcy forced convection in a fluid-saturated porous medium tube under...     

Vertical Impact on a Rigid Body Floating on the Surface of an Ideal Incompressible Fluid in a Bounded Basin of Arbitrary Shape

In the case of basin walls located at a large distance from the body, the asymptotics of the main impact parameters are found. As concrete examples, impact problems for regions with spherical boundaries are considered.     

Undular Jump in Open‐Channel Flow Over a Sill

The paper reports experimental data on a steady flow with a free surface over a rectangular sill at the bottom of a rectangular channel. The paper focuses on the parameter range in which a qualitative change in flow pattern accompanied by formation of an undular jump is observed. It is shown that transition from the bottom state the surface state of head and tail conjugation to occurs when the second critical depth is reached over the downstream edge of the sill. Conditions of transition from a free state to a submerged state of flow over the sill are considered; conditions of validity of the assumption that the first critical depth is reached over the sill are discussed.     

Instability of a Cantilever with a Propeller in an Incident Flow

A physical explanation is given to the mechanism of back coupling of the perturbed motion of a propeller in its plane of rotation and the force in the same plane. This unusual feedback may cause a mechanical system with a propeller to self-excite in the plane of possible oscillations of its axis upon propeller reversal. Instability occurs easier at the resonance of the system when the resultant moment of external forces lags in phase behind the angle of attack by approximately 5/4.