Multi-resolution wavelet basis for solving steady forced Korteweg–de Vries model

A steady forced Korteweg–de Vries (fKdV) model which includes gravity, capillary, and pressure distributions is solved numerically using the wavelet Galerkin method. The anti-derivatives of Daubechies wavelets are developed as the basis of the solution subspaces for the mixed boundary condition type. Accuracy of numerical solutions can be improved by increasing the number of wavelet levels in the multi-resolution analysis. The theoretical result of convergence rate is also shown. The problem can be viewed as gravity-capillary wave flows over an applied pressure distribution. The flow regime can be characterized by subcritical, supercritical, and critical flows depending on the value of the Froude number. Trapped depression and elevation waves are found over the pressure distribution. For a near-critical flow regime, a generalized solitary wave with ripples is presented. This shows a capillary effect in balance to gravity and the pressure force on the free surface.

Modern vision for critical flow in an egg-shaped section

The critical regime plays a primordial role in the study of gradually varying flows by classifying flow regimes and slopes. Through this work, a new approach is proposed to analyze critical flow regime in an egg-shaped channel. Based on both the definition of Froude number and Achour and Bedjaoui general discharge relationship, a relation between critical and normal depths is derived and then graphically represented for the particular case of a smooth channel characterized by a generating diameter equal to one meter. The results show the influence of the slope on the frequency of occurrence of the critical regime. At the same time and independently of the flow rate, a very advantageous approach for the calculation of the Froude number has been proposed. The study shows that there are six zones to differentiate the various flow states, namely: on the one hand for steep slopes two subcritical zones interspersed by a supercritical zone and on the other hand for mild slopes a zone corresponding to uniform flow, an area where the flow is probably gradually varied and finally an area where the flow is abruptly varied. Based on the specific energy equation, a validation process concluded that the proposed relationships were reliable.

Fluid dynamics around three cylinders in presence of small control cylinders

A numerical study is performed to analyze the effect of small control cylinders on fluid force reduction and vortex shedding suppression on the flow past three inline square cylinders using the lattice Boltzmann method. The Reynolds number Re = 160 is fixed while the spacing between the cylinders is taken in the range of 1.0D ≤ g* ≤ 5.0D (where D is the size of the main cylinder) and the control cylinder size is varied from 0.1D to 0.5D. To systematically understand the effect of control cylinders on the forces, a detailed analysis of Strouhal number (St), mean drag coefficient (CDmean), and root mean square values of the drag and lift coefficients is presented in this paper. In this study, it is observed that the average mean drag coefficient (CDmeanaverage) and Strouhal number reached either maximum or minimum values at different values of separation ratio (g*) and small control cylinder size (d). It is found that at (g*, d) = (5.0, 0.0) and (1.0, 0.5), the average CDmean attains its maximum (CDmeanaverage = 0.7813) and minimum (CDmean = 0.0988) values. Furthermore, at (g*, d) = (5.0, 0.3) and (2.0, 0.0) the average St attains its maximum (St = 0.1780) and minimum (St = 0.041) values. It is found that the flow regimes completely change in the presence of control cylinders. In particular, at g* = 4.0 there is a critical flow regime when the size of the control cylinder changes from 0.1 to 0.5. The sudden jump in the mean drag coefficient and Strouhal number for the middle cylinder with their maximum and minimum values also confirms the critical flow regime. The effect of control cylinders within tandem square cylinders has not been studied before.

Argumentation for critical parameters and operating modes in the process of underwater mining of placers

The purpose of the article is to study the connection between the parameters of the formation of the suction funnel, such as the scattering speed and concentration of the suction mixture, and the concentration of the slurry in the suction pipe, which provides supercritical flow conditions. This connection is considered in terms of the most common process of underwater mining of placers for the open mining technology by suction dredger. The importance of the research is conditioned by the well-known but not yet thoroughly studied phenomenon of a decrease in the performance of the dredger pump on solid material without breaking the vacuum, which in most cases leads to a hydraulic shock in the pressure line. It is argued that the cause of this occurrence is the onset of a critical flow regime in the suction pipe due to inconsistency of the parameters of the hydrotransport modes and suction funnel formation. A combined analysis of the known dependences for the critical rate of hydro transportation in an inclined pipeline and for the geometric parameters of the suction funnel made it possible to establish restrictions on the concentration of solid particles on the surface of the erosion funnel.

The conditions for occurrence of critical flow regime of water in the open stream

For the solution of engineering problems require increasingly accurate estimates of the hydraulic characteristics of the water streams. To date, it is impossible to consider sufficiently complete theoretical and experimental justification of the main provisions of the theory of turbulence, hydraulic resistance, channel processes. The composition of tasks related to flows in wide channels, turbulence problems are of scientific and practical interest. Various interpretations of the determination of the critical Froude number in wide open water flows based on observations and theoretical transformations are considered. The conditions for the emergence of a critical regime of water flow in an open wide channel are analyzed in order to estimate the critical Froude number and critical depth. Estimates of the critical Froude number for laboratory and field conditions are given. The estimations allow us to consider the proposed approach acceptable for determining the conditions of occurrence of the critical flow regime. The General, physical interpretation of conditions of occurrence of the critical regime of water flow on the basis of phenomenological approach is specified. The results take into account the values of the components of the total specific energy of the section. This shows the estimated calculation. The results obtained theoretically make it possible to compare the above interpretations and determine their applicability, and the results of the analysis can be useful for the estimated calculations of flows in channels and river flows in rigid, undeformable boundaries and with minor channel deformations.

Numerical Simulation on the Aerodynamic Characteristics Effect of Ribs Acting on the Cooling Tower

The experimental work deals with the modelling of flow around a two-dimensional model of an infinite cylinder in a trans-critical flow regime. Herein, there was used ANSYS Fluent and the turbulent model k-ε realizable for the calculation of the pressure distribution around the cylinder. This turbulence model belongs to Reynolds Averaged Navier-Stokes equations (RANS). The simulated numerical domain considered half of the cylinder with the diameter of 70 m, wind flow was set to 35 m.s-1, which resulting in the Reynolds number of Re = 1,68.108. In this study, meridional wind ribs were modelled physically. A parametric study was modelled with the different shape of ribs, ribs spacing and height. Simulated results were compared with experimentally ascertained data and guidelines.

Water Level Rise Upstream a Permeable Barrier in Subcritical Flow: Experiment and Modeling

This work addresses the dependence of water depth upstream a permeable barrier, h1, with discharge per unit channel width, Q/W, in sub-critical flow regime. The barrier, that extends over the entire width of the channel, is composed by smooth cylinders of small aspect ratio vertically mounted on the bottom in a staggered pattern and fully submerged in the flow. The height of the cylinders above the bottom was kept constant for all runs. Several configurations were considered by varying systematically the cylinders diameter, dv, the number of cylinders per unit area of the bed, or density, m, and the length of the barrier in the stream direction, Lv. A one-dimensional model was developed to predict the observed values of h1 and to obtain a sound basis taking into account the incidence of Q/W, m, dv and Lv. This model is based on fluid mechanics equations applied on a finite control volume for the flow in the test section, and it was deduced under simplifying assumptions physically-based. Finally, and based on the experimental results and the model predictions, the mechanical energy losses of the flow are analyzed. The main role played by a dimensionless number R, that takes into account the barrier's resistance to the flow, is highlighted.