Channel Of Variable Cross Section Research Articles

Experimental study of the effect of air oscillations on vapor diffusion in a channel of variable cross-section and in a granular medium

The diffusion of 2-propanol vapor in the air in a channel of variable radius and in a porous medium composed of spheres of equal diameter under longitudinal oscillations is experimentally studied. In the experiments, vapor concentration at the top and bottom of the channel (or porous medium) is constant. In the absence of oscillations, mass transfer along the channel (or porous medium) is carried out due to molecular diffusion. When air oscillations are imposed, additional mass transfer effects are activated, namely, Taylor dispersion and convective mass transfer due to steady vortex flows. In the studied range of frequencies and amplitudes, the total mass transfer exceeds molecular diffusion by one order of magnitude. In a channel of variable radius, mass is transferred mainly due to the steady vortex flows (convective mass transfer) arising in the viscous boundary layer due to the inhomogeneity of the amplitude of air oscillations in narrow and wide sections of the channel. In a porous medium, Taylor dispersion plays a major role while the convective mass transfer makes minor contribution.

Application of the Three-Parameter Differential Model of Turbulence for Solving Problems of Flow and Heat Transfer in Channels of Variable Cross-Section. Part 1

A description of the method of numerical study in the approximation of a narrow channel of the problems of flow and heat transfer in flat and circular channels of variable cross-section using a differential three-parameter model of shear turbulence is presented. The main results of numerous studies using the proposed method are described, one of the goals of which was to substantiate the possibility of using the narrow channel approximation. This review study is carried out in two parts. In the first part the results of studies of mixed convection in vertical pipes under conditions of stable and unstable stratification, as well as flows in channels with permeable walls in the presence of blowing or suction on the wall, are presented.

Localization and Spreading of Asymptotic Solutions of a Hyperbolic Equation with Variable Coefficients Describing Waves in a Channel of Variable Cross Section

Asymptotic solutions of the Cauchy problem with localized initial conditions are described for a hyperbolic equation describing waves in a channel of variable cross section. It is shown that, if the equation is reduced to a wave equation, then the solution remains localized, whereas, if the initial equation reduces to the Klein–Gordon equation, then nonlocalized corrections occur in the asymptotics.

ВЛИЯНИЕ РАЗМЕРНОСТИ МАТЕМАТИЧЕСКОЙ МОДЕЛИ ВНУТРЕННЕЙ БАЛЛИСТИКИ НА РАСЧЕТНЫЕ ПАРАМЕТРЫ ВЫСТРЕЛА ДЛЯ ЗАРЯДОВ ИЗ ЗЕРНЕНОГО ПОРОХА

The problem of the impact of the mathematical model dimension on the calculated intraballistic characteristics of a shot for the charges made of granulated powder is considered. Mathematical models of the shot are studied using the spatial (axisymmetric), one-dimensional, and zero-dimensional (thermodynamic) formulations. The thermodynamic model takes into account the distribution of the pressure and velocity of a gas-powder mixture behind the shot for a channel of variable cross-section. Comparison of simulation results is carried out in a wide range of loading parameters. It is shown that there is a range of the loading parameters for a thermodynamic approach to give satisfactory approximation to the parameters obtained using the gas-dynamic approach, which describes the flow of a heterogeneous reacting mixture with a separate consideration of phases and intergranular interactions between them. Notably that in the entire range of the charging parameters studied in this work, the one-dimensional and twodimensional gas-dynamic models only slightly differ from each other. Therefore, in the main pyrodynamic period, the actuation of the charge, made of granulated powder, can be simulated using a one-dimensional gas-dynamic model or a zero-dimensional thermodynamic model with allowance for spatial distribution of the pressure and velocity of the gas-powder mixture.

Dynamics of Detonation Waves in Cylindrical Channels of Variable Cross Section

A bubble liquid with a fuel mixture of gases is an explosive in which a detonation wave with an amplitude to 100 atm may appear on exposure to a pressure pulse of about 10–20 atm. The mass calorific value of such an explosive is six or more orders of magnitude lower than that of regular solid, liquid, and gaseous explosive materials. Furthermore, in fuel liquids containing curtains with vapor-air bubbles, sharp jerks during the transportation may contribute to the formation of detonation waves leading to emergencies. Therefore, studying detonation waves in bubble media is of interest from the viewpoint of ensuring explosion safety and from the viewpoint of the problem of transmission of information in the liquid in the form of waves. In the present work, a numerical study is made of the propagation of detonation waves in a cylindrical channel with a sudden expansion, which is filled with bubble liquid. Possible scenarios of the dynamics of detonation waves once they pass into the channel′s expanding part are analyzed. The influence of the volume content of the fuel gas and of geometric parameters of the channel on the propagation and separation of a detonation wave is established. It is shown that there can be two regimes of propagation of detonation on passage of a detonation wave into the expanding zone: continuous propagation of detonation and separation of detonation.

Steady Flows of a Fluid Oscillating in an Axisymmetric Channel of Variable Cross-Section, Versus the Dimensionless Frequency

The averaged flows excited by oscillations of fluid in an axisymmetric channel, which transverse section periodically changes with longitudinal coordinate, are experimentally studied. Oscillations are caused by harmonious change of a volume of the fluid, which is pumped over via the channel. Researches are executed within the broad range of dimensionless frequency which characterizes the ratio of the cross size of the channel to the thickness of Stokes boundary layers. It is shown that oscillations of fluid excite an averaged flows in the form of a system of toroidal vortex structures in each segment of the channel. The intensity of averaged flows increases with the increase in amplitude and frequency of fluid oscillation and is defined by the pulsational Reynolds number and the dimensionless frequency in the channel of the set geometry. It is shown that in the limit of low dimensionless frequencies, when viscous forces define the oscillating component of flow in the whole channel, the primary vortices occupy all the volume of the channel. The cross size of the primary vortices decreases with the increase in dimensionless frequency, and at high frequencies the vortexes are localized in viscous boundary layer near the side border in a narrow part of the channel. At the same time, the secondary vortices having opposite turning are formed outside the primary boundary layer vortexes in the bulk of the channel. The transformation of the structure of averaged flows and their intensity versus the dimensionless frequency are studied.

Stability of One-Dimensional Steady Flows with Detonation Wave in a Channel of Variable Cross-Sectional Area

The stability of one-dimensional steady flows of an ideal (inviscid and non-heat-conducting) gas in channels of variable cross section with combustion in a structurally stable detonation wave is studied. The detonation wave represents a discontinuity surface propagating normally to the axis of the channel. It was previously established that, in this formulation, steady flows with combustion in a Chapman–Jouguet detonation wave are always unstable, in contrast to combustion flows in an overcompressed detonation wave. The stability analysis of such flows is reduced to the numerical solution of an initial-boundary value problem describing the evolution of finite flow perturbations between the moving detonation wave and the minimal nozzle cross section (in the case of a sudden contraction) or the exit nozzle cross section. The problem is solved by applying a modified Godunov scheme of higher order accuracy. More specifically, a Riemann solver with switching (between the overcompressed and Chapman–Jouguet detonation waves) with an explicitly represented detonation wave is created. Examples of stable flows and flows collapsing due to large initial perturbations are given, and their dynamics with transitions to a Chapman–Jouguet detonation wave and back are computed.

Flow of a Two-Phase Vapor-Droplet Mixture in a Variable Cross Section Channel with Phase Transitions

The features of a two-phase vapor-droplet flow in a convergent-divergent (Laval) nozzle are studied in the quasi-one-dimensional formulation with allowance for phase transitions. The effect of the governing parameters (the concentration and diameter of dispersed drops, etc.) on the mixture flow was studied in a wide range. The calculations were performed for both subcritical and critical mixture flows. The regularities of a two-phase mixture flow in different critical flow regimes are examined. The effect of governing parameters on the critical (maximum) mixture flow rate is analyzed.

The Instability of Steady-State Flows with a Chapman—Jouguet Detonation Wave in a Channel of Variable Cross Section

This work investigates the stability of steady flows of ideal (inviscid and nonconductive) gas in channels with variable cross sections, in the diverging part of which a Chapman-Jouguet detonation wave (DWCJ) is located. Steady and unsteady flows are described by equations in a one-dimensional approximation with the detonation wave represented by a planar discontinuity surface, normal to the channel axis. The combustible mixture before the detonation wave and the combustion products behind it are perfect gases with constant heat capacities, which, like additive constants in terms of the internal energy and enthalpy, are different before and after the wave. Since the Mach number behind the DWCJ is equal to unity, it can stand only in the diverging part of the channel in the steady flow. Moreover, depending on the conditions at the channel exit, the flow behind it can be either super- or subsonic. In the first case, the initial Pertubation can reach the DWCJ only from the left (the gas moves from left to right), and, in the second case it can come from both sides. When investigating the stability, is it is assumed, first, that after the initial perturbation, the detonation wave, which is slightly shifted, remains a DWCJ. In this case, analysis of stability reduces to calculating the derivative of the Mach number of DWCJ from the Mach number of the steady flow in front of the wave. In this formulation, the derivative value is always such that the flow under consideration is unstable. Small perturbations of the DWCJ make it slightly overcompressed. However, even taking this into account, a steady flow with a DWCJ in a diverging channel is always unstable.

Моделирование течения газа в каналах переменного сечения при различных режимах течения методом решеточных уравнений Больцмана (LBM)

All contact-free vacuum pumps operate in a very wide pressure range. Therefore, the calculation of flows through the slot channels is associated with the need to take into account the laws of all three modes of gas flow: viscous, transitional and molecular. Most of channels of contact-free pumps are formed by curved walls, which are slits of variable cross-section in the direction of gas flow, having a minimum gap in some place. The paper considers the basic methods of calculating flows in channels of variable cross-section: the Monte Carlo method for molecular mode, the numerical solution of Navier --- Stokes equations for viscous mode and the Lattice Boltzmann method (LBM) for a wide range of pressures. The results of gas flow simulation calculated in COMSOL Multiphysics with LBM method are presented. The influence of the gas flow mode on the velocity profile in the channel is discussed. Based on the simulation results, the conductivity of channels of different geometries was calculated at various pressures at the inlet and outlet of the channel. The graphs of conductivity dependence on the Knudsen number for the method of angular coefficients, the model of lattice Boltzmann equations and experimental data are presented. It is shown that for slit channels of variable cross-section, the LBM model agrees well with the experiment under any gas flow modes.

Features of fibrous materials agglomeration in flat-matrix granulators

From the standpoint of ensuring the receipt of the recycled bodies for various technological purposes with standard and improved properties applicable in construction, petrochemistry, metallurgy and other areas of material production, recycling in the field of agglomeration of fibrous man-made materials is relevant. The article is devoted to the theoretical studies of the fibrous materials agglomeration characteristics in flat-matrix granulators-extruders with the channels of variable circular cross-section. Taking into account the analysis of the well-known calculation methods and as a result of the theoretical studies, the general regularities have been revealed and the equations have been proposed for determining the equilibrium conditions of a deformable material layer and changes in pressure in the channel, taking into account the effect of the operating device and fiber properties. Analytical dependences and changes in the axial pressure along the channel are obtained reflecting the regularities of the fibrous material movement.

Dispersive and dispersive-like bores in channels with sloping banks

In this paper a detailed analysis of undular bore dynamics in channels of variable cross-section is presented. Two undular bore regimes, low Froude number (LFN) and high Froude number (HFN), are simulated with a Serre–Green–Naghdi model, and the results are compared with the experiments by Treske (1994). We show that contrary to Favre waves and HFN bores, which are controlled by dispersive non-hydrostatic mechanisms, LFN bores correspond to a hydrostatic phenomenon. The dispersive-like properties of the LFN bores is related to wave refraction on the banks in a way similar to that of edge waves in the near shore. A fully hydrostatic asymptotic model for these dispersive-like bores is derived and compared to the observations, confirming our claim.

Numerical simulation of fuel combustion in stationary detonation wave in variable cross-section channel with supersonic flow at the inlet and outlet

Numerical simulation of fuel combustion in stationary detonation wave in variable cross-section channel with supersonic flow at the inlet and outlet

Calculation of unsteady two-phase quasi-onedimensional channel flow based on the two-fluid model and the artificialviscosity numerical scheme

An example of usage of the artificial viscosity technique for numerical simulation of unsteady one-dimensional two-phase flows based on the two-fluid approach is presented. The governing equations system is written under assumption of equal pressure in the fluids. No interfacial exchange is taken into account. Performance of the artificial viscosity technique suggested has been evaluated via numerical solution of a model problem of two-phase flow in a channel of variable cross-section. It has been shown that the used numerical scheme, implicit and first-order, involving the suggested artificial viscosity model, provides a stable process of getting a numerical solution and predicts a physically adequate flow dynamics without non-physical oscillations.

Flow resistance in a variable cross section channel within the numerical model of shallow water

The resistance to a flow in open channels of river type depends on a variety of parameters. The coefficient of bottom roughness is an integral quantity accounting for the geometric and physical features of the river bottom. Definition of the channel cross-section variability contribution to the roughness coefficient is the aim of our research. We have applied the 2D numerical model of surface water dynamics in the shallow water approximation to our task. The Manning roughness coefficient for non-prismatic open channels has been estimated depending on the parameters of the variable cross-section of the water flow in the range n = 0 ÷ 0.02.

Modeling of glow discharge in longitudinal gas flow in a plane channel of variable cross section

A two-dimensional model of glow discharge positive column in gas flow has been suggested in this paper. It is considered that the discharge maintained between the permeable mesh electrodes installed in the initial and end sections of the plane channel. In general case the channel width changing along the stream is accounted. The positive column in gas flow is described by integro-differential system of equations with an approximation of constant gas flow density. The border conditions for gas ionization degree and temperature in the initial section of channel are given by any functions. An analytical solution of that system was obtained and special cases of the boundary conditions analyzed.

English

The purpose of this paper is to present a technique of variable cross section conformal cooling channels (VCCC) to compare the cooling effect of moulds with equal section channel experimentally. The influence of the size structure parameters of the variable cross section conformal cooling channel on heat transfer is studied. It is found that the ratio of D/d=1.4 has the best effect of enhanced heat transfer. To determine the better heat transfer effect of variable cross section channeli¼Œthis paper studies the influence of variable cross section channel and traditional equal section channel on heat transfer and takes temperature distribution, pressure drop and water velocity as evaluation indexes. In addition, in order to further discuss the effect of the conformal cooling channel structure, the influence of the opposite direction channel arrangement and the same direction arrangement on the heat transfer is studied. It is found that the adjacent channel of the opposite direction arrangement has better heat transfer effect and cooling uniformity. Key words: Equal section channel, variable cross section channel, conformal cooling, enhanced heat transfer.

Lattice Boltzmann method simulations about shale gas flow in contracting nano-channels

Shale matrix consists of numerous interconnected nanoscale slit pores with size ranging from 4 nm to 200 nm, naturally resulting in variable cross-section scenarios for shale gas transport. Understanding the behavior of shale gas flow in variable cross-section channels would have practical benefits to further reveal the gas flow mechanism. Herein, using multiple-relaxation time lattice Boltzmann method (LBM) simulations, we investigate the flow characteristic of shale gas in sudden and gradual contraction channels. The influences of Knudsen number and cross-section shrinking coefficient on the shale gas transport are discussed in details. We find that the relationship between centerline velocity and Knudsen number is dependent on the gas flow regime. The nonlinear pressure deviation shows a negative correlation with the Knudsen number. The slip mass flux and the second-order permeability correlation factor are found to have positive correlations with the cross-section shrinking coefficient, demonstrating that the shale gas apparent permeability would be underestimated without considering the influence of cross-section contraction. Moreover, we reveal that the shrinking of pore channel has a great influence on Knudsen minimum effect. A high cross-section shrinking coefficient and dramatically varied cross-section type will lead to a low critical Knudsen number of Knudsen minimum effect. The LBM results and insight obtained here would be conductive to understanding shale gas transport in contracting nano-channels.

Numerical Study of Detonation Wave Propagation in the Variable Cross-Section Channel Using Unstructured Computational Grids

The work is dedicated to the numerical study of detonation wave initiation and propagation in the variable cross-section axisymmetric channel filled with the model hydrogen-air mixture. The channel models the large-scale device for the utilization of worn-out tires. Mathematical model is based on two-dimensional axisymmetric Euler equations supplemented by global chemical kinetics model. The finite volume computational algorithm of the second approximation order for the calculation of two-dimensional flows with detonation waves on fully unstructured grids with triangular cells is developed. Three geometrical configurations of the channel are investigated, each with its own degree of the divergence of the conical part of the channel from the point of view of the pressure from the detonation wave on the end wall of the channel. The problem in consideration relates to the problem of waste recycling in the devices based on the detonation combustion of the fuel.

Nonlinear wave dynamics in self-consistent water channels

We study long-wave dynamics in a self-consistent water channel of variable cross-section, taking into account the effects of weak nonlinearity and dispersion. The self-consistency of the water channel is considered within the linear shallow water theory, which implies that the channel depth and width are interrelated, so the wave propagates in such a channel without inner reflection from the bottom even if the water depth changes significantly. In the case of small-amplitude weakly dispersive waves, the reflection from the bottom is also small, which allows the use of a unidirectional approximation. A modified equation for Riemann waves is derived for the nondispersive case. The wave-breaking criterion (gradient catastrophe) for self-consistent channels is defined. If both weak nonlinearity and dispersion are accounted for, the variable-coefficient Korteweg–de Vries (KdV) equation for waves in self-consistent channels is derived. Note that this is the first time that a KdV equation has been derived for waves in strongly inhomogeneous media. Soliton transformation in a channel with an abrupt change in depth is also studied.