Pipe Of Rectangular Cross-section Research Articles

A snake robot for locomotion in a pipe using trapezium-like travelling wave

Snake robots are a suitable solution for various types of applications, especially in rough terrain or hardly accessible areas such as, for example, pipes. This article deals with a snake robot moving in a pipe using a so-called trapezium-like travelling wave. In this paper, we present a mathematical model of locomotion of the snake robot in a pipe of rectangular cross-section. Subsequently, we designed a control algorithm using a trapezium-like travelling wave. Within the control algorithm we introduced the so-called motion matrix of a trapezium-like travelling wave that contains information about the vector of generalized variables at any point of the locomotion cycle. The paper also presents a simulation model in MATLAB R2019b interfacing with CoppeliaSim V4.0.0. Furthermore, in our research we have developed an experimental snake robot with the purpose to verify the derived mathematical model, control algorithm and simulation model. Experimental results show the influence of certain parameters of the trapezium-like travelling wave on locomotion properties, such as the travelled distance or the average speed of the snake robot passing through a pipe. In the final part of this paper, experimental results are discussed and key elements of the proposed control algorithm are highlighted.

Three-dimensional analysis of heat transfer in a channel provided with solid baffle, single and double perforation

PurposeThe purpose of this paper is to present a three-dimensional (3D) analysis of the laminar flow of air and the conjugate heat transfer in a pipe of rectangular cross-section with a solid or perforated deflector inserted on the lower wall.Design/methodology/approachTo this end, by using the finite volume method, the conservation equations for mass, momentum and energy are solved numerically. Two cases of “single and double” perforation were studied and compared with that of the solid case for a range of Reynolds numbers ranging from 140 to 840. The velocity and temperature profiles were plotted and interpreted on three different sections placed sequentially upstream, mid-stream and downstream of the deflector. Total heat exchange at the bottom wall, outlet fluid temperature, perforated PFE deflector performance and pressure loss is presented for different cases studied and for different Reynolds numbers.FindingsThe results show that although the perforated deflector improves the heat transfer, it also results in additional pressure losses; the study also showed the existence of a limiting velocity beyond which the perforation effect on the improvement of the heat exchange decreases until the same performance of the solid deflector is achieved.Originality/valueThe main originality of this work is to show a 3D analysis for a perforated baffle as heat exchanger application.

Induction heating simulation of the waveguide assembly elements

The waveguide path systems consisting mainly of aluminum alloys with improved weight, size, and electrical parameters are used to ensure the functioning of the spacecraft and its onboard equipment in accordance with a given program. When assembling the elements of the waveguide paths, in particular a thin-walled pipe of rectangular cross section, coupling and flange, induction brazing is used. Element-by-element assembly of lightweight waveguide paths using the method of induction soldering is connected with a number of technological difficulties such as the uneven distribution of temperature fields, the thickness variation of the soldered products and the design features of the inductors. This paper presents a model describing the process of heating a pipe-inductor system during induction brazing. The presented model describes the process of induction heating of the pipe as a separate structural element of the waveguide path. In the process of simulation in the Comsol software, on the basis of numerical simulation methods with the connection of the necessary media involved in induction heating, the pipe heating graphs are obtained.

Функція Гріна конвективного хвильового рівняння для нескінченної прямої жорсткостінної труби прямокутного поперечного перерізу

Функція Гріна конвективного хвильового рівняння для нескінченної прямої жорсткостінної труби прямокутного поперечного перерізу

Laminar instability of pressure-driven dynamos in multiple helical pipes

Dynamo action is considered in a network of intertwined, helical pipes of rectangular cross-section. The flow in each pipe is driven solely by a pressure gradient and it is assumed that both the velocity and magnetic fields remain helically symmetric as the system evolves. The exact laminar solution is followed into the nonlinear regime. In a previous study, it was found that two such pipes produced a satisfactory dynamo. However, purely hydrodynamic instabilities were found to lead to flow configurations which did not support even a kinematic dynamo. The dynamo therefore only functioned at magnetic Prandtl numbers greater than unity. In this paper, it is shown that a multi-pipe configuration drives the dynamo at a significantly lower Prandtl number. A different flow instability is observed, which is found not to inhibit magnetic field generation. A model of the flow instability is considered by analysing the Dean equations for a low-aspect-ratio rectangle. The resultant quasi-one-dimensional flow gives rise to two linked stability equations of Orr–Sommerfeld type. The inflection point in the cross-pipe secondary flow is found to drive the new instability, with the downpipe primary flow having little influence.

Experiments on standing bubbles in a vertical pipe

We present a series of laboratory experiments in which a steady stream of air is supplied through a small hole in the wall of a vertical pipe of rectangular cross-section down which there is a steady flux of water. For a range of liquid flow rates, the air forms a steady standing bubble whose nose is attached to the point of air supply. The steady bubble sheds a flux of much smaller air bubbles at its base, located downstream of the air injection point. The minimum liquid speed for which steady standing bubbles develop occurs at a particular Froude number of the liquid flow, Frd = U/$/sqrt{\it gd}$ = 0.38, where U is the upstream speed, g the acceleration due to gravity and d the width of the cell. These trapped bubbles are distinct from the freely rising Taylor bubble, in that the Froude number at the nose is variable. Also, on a length scale greater than that influenced by surface tension, we find that the bubble nose asymptotes to a cusp-like shape, with an angle that decreases with Frd. We show that numerical solutions of the potential flow equations replicate the bubble shape and angle of the cusp, which appear independent of the gas flux. We also find that there is a minimum gas flux for which these standing bubbles develop. As the gas flux decreases below this threshold, the standing bubbles become unstable and, instead, a much shorter oscillating bubble develops. This produces a wake which has similarities with that formed downstream of a cylinder in a confined channel, but which also carries bubbles downstream. We also find that with sufficiently small gas flux, no bubble develops. For liquid flow rates smaller than the critical value, Frd < 0.38, we find that the bubbles become unstable and detach from the injection point and rise up the tube.

Thermocapillary migration of long bubbles in polygonal tubes. II. Experiments

We study experimentally the thermocapillary migration of a long gas bubble in a horizontal pipe of rectangular cross section. An imposed axial temperature gradient produces a gradient of surface tension leading to a steady migration of the bubble towards the hotter region. The bubble velocity is found to be independent of bubble length for sufficiently long bubbles, and to vary linearly with the temperature gradient. For pipes of small vertical dimension, gravity is negligible and the measurements of the bubble velocity are in good agreement with the zero gravity theory of Mazouchi and Homsy [Phys. Fluids 13, 1594 (2001)]. In larger pipes, gravity is no longer negligible and the bubble is observed to move faster than that theory predicts. A simple calculation taking into account the combined effect of buoyant rise and thermocapillary stress accounts for these results.

Streaming current development in a rectangular channel

In this paper, we fast analyse the flow distribution in a metallic pipe of rectangular cross section. In the case of a laminar flow, an analytical solution has been found for the velocity distribution in the pipe cross section. Concerning the space charge density profile, in the case of weak space charge density in the whole section, the general system of equations for a rectangular channel have first been solved. Thus, the space charge density profile can be expressed in terms of the channel dimensions, the diffusion constants and the total charge in the diffuse layer, which is an indicator of the diffuse layer development. Indeed, in the case of a diffuse layer development controlled by a weak wall current ( as it is very often the case ), the space charge density profile is close to a quasi fully developed diffuse layer profile for which the total charge in the diffuse layer increases slowly in order to reach a constant value. Then, the space charge density convected in a such rectangular pipe has been computed, in terms of the geometry of the pipe and the state of development of the diffuse layer, that is to say, in terms of the total space charge in a given cross section. In the case of a turbulent flow, an analysis shows that in our experimental results, a large part of the diffuse layer is perturbed by the turbulence even for a relatively low Reynolds number. Therefore, the space charge density convected in a given cross section is nearly proportional to the mean space charge density in the whole section, or the total charge in this section. Thus, the mesurement of the space charge density convected in a given section indicates the mean space charge density in that section, and so the state of development. We present new experimental streaming current results for a rectangular channel. The experiments were conducted for Reynold's numbers varying from 2000 to 5000 and channel lengths from the entry of the pipe varying from a few centimeters to one meter. These results give the evolution of the space charge density development for different Reynolds numbers and for different lengths from the entry of pipe.

Freeze/thaw characteristics of a copper/water heat pipe - Effects ofnoncondensible gas charge

The freeze/thaw characteristics of a copper/water heat pipe of rectangular cross section were investigated experimentally to determine the effect of variations in the amount of noncondensible gases present. The transient internal temperature profiles in the liquid channel are presented along with contours of the frozen fluid configuration obtained through visual observation

Fundamental Equations Governing Pressure Surge Phenomena in Pipes of Rectangular Cross-Section

The two fundamental principles, momentum and continuity, which govern the behaviour of pressure surge phenomena, are developed for pipes of rectangular cross section. A theoretical relation for the velocity of propagation of a pressure surge in such pipes is also obtained. It is represented in a chart for various pipe-wall materials, and comparisons made with experimental data. In addition, the deflection of the wall of a square section pipe is examined, theoretically and experimentally.

Effect of Wall Material on Organ-Pipe Tone—An Evaluation of Some Earlier Experiments

Dayton C. Miller has described experiments on a double-wall organ pipe of rectangular cross section in which the space between the wails could be filled with water, producing substantial alterations in pitch and tone [Science 29, 161 (1909)]. These experiments have been quoted by Miller and others as demonstrating the influence of the wall material on the tone quality of woodwind instruments. Calculations of the elastic deformations to be expected under internal pressure show that Miller's results are due to the rectangular cross section of his pipe and would be absent for one of circular cross section. This result was verified in this laboratory by constructing a double-wall cylindrical organ pipe, for which no measurable changes in tone were produced when the space between the walls was filled with water. This result is also verified by the experiments of Boner and Newman on cylindrical organ pipes [J. Acoust. Soc. Am. 12, 83 (1940)]. The small differences in pitch and quality among the thinner pipes noted by these authors can be explained by assuming the pipes to have a slightly elliptical cross section. For cylindrical organ pipes of reasonable wall rigidity, the steady-state tone quality should not depend on the wall material.

On some types of flow of a conducting fluid in pipes of rectangular cross-section, placed in a magnetic field

We examine the solution of the integral equations for the problem of the steady flow of a conducting fluid in a rectangular pipe with two non-conducting walls and two conducting walls, the latter in planes parallel to the outside magnetic field. Also, we give a new form of the solution of Shercliff's [1] problem of flow in a pipe with non-conducting walls. The actual solutions given are valid, in particular, also for large values of Hartmann number.

Calculation of the Pressure Gradient along a Pipe of Uniform Cross-section

It is difficult to solve the differential equation determining the velocity distribution in a pipe of uniform cross-section, which has complicated boundaries. One of the methods of solution in such cases is to use the variational principle. When the quantity of flow is given, the functional which gives an approximate value of the pressure gradient along the axis greater than the true value is already known. The authors have got the functional which gives an approximate value smaller than the true value. Using these two values, it is .possib1e to determine the region in which the true value exists. As examples, the pipe of rectangular cross-section and the pipes of circular cross-section with one or two inside cores of circular cross-section are treated.

Wave Guides and the Special Theory of Relativity

The Lorentz transformation is applied to the H01 solution of Maxwell's equations used to describe wave propagation in conducting pipes of rectangular cross section. When group velocity for the wave is employed in the transformation, the solution obtained is that one characterizing wave-guide operation at cut-off frequency, thus demonstrating that the speed associated with power or signal transmission is group velocity. When phase velocity for the wave is employed in the transformation, and we treat all quantities appearing in the new solution as real, we find that the problem has been reduced to one in magnetostatics and the significance of this solution is pointed out. The use of the inverse Lorentz transformation to find wave guide solutions from known solutions of problems in statics is indicated.

Rectangular Hollow-Pipe Radiators

The open hollow pipe of rectangular cross section is discussed from both practical and theoretical standpoints as a radiator and absorber of ultra-short electromagnetic waves. A theory of operation is derived and it is verified by a series of measured radiation patterns taken at wavelengths of 50 to 100 centimeters.

Electromagnetic Waves in Hollow Metal Tubes of Rectangular Cross Section

The theory of the transmission of electromagnetic waves in hollow conducting pipes of rectangular cross section is derived for perfectly conducting and for imperfectly conducting materials. Special attention is given to the type of wave that has only one transverse and everywhere parallel component of electric intensity, and the results of experiments on this wave are reported. Expressions for the attenuation of the different types of waves allow comparisons to be made with corresponding waves in a pipe of circular cross section. In a rectangular pipe, no wave has been found whose attenuation decreases indefinitely as the frequency is increased, as does the H <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</inf> wave in a circular pipe.

Flow in a pipe of rectangular cross-section

The object of the research was to investigate the flow of water in a pipe of rectangular cross-section. Much work has been done on similar problems with pipes of circular section, and pipes of rectangular section have been investigated by Fromm and Davies and White. Fromm avoided with pipes in which the ratio of the sides was never less than 6 to 1; his report deals only with turbulent flow. In the case of Davies and White's research, the minimum ratio of the sides was 40 to 1, so that the laminar flow could be calculated from the formula for flow between infinitely wide parallel plates. The present writer used a pipe of section 1·178 cms. by 0·404 cms, (ratio of sides = 2·92); this presents a fresh problem were stream line flow is concerned, and shows interesting results in the region of the critical velocity.