Tube Of Rectangular Cross Section Research Articles

SPH simulations and experimental investigation of water flow through a Venturi meter of rectangular cross-section

The flow of water through a horizontal small-scale Venturi tube of rectangular cross-section is simulated using a modified version of the open-source code DualSPHysics, which is based on Smoothed Particle Hydrodynamics (SPH) methods. Water is simulated using the Murnaghan-Tait equation of state so that weak compressibility is allowed. The hydrodynamics is coupled to a Large-Eddy Simulation (LES) turbulence model. The convergence properties of SPH are improved by adopting a C2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{2}$$\\end{document} Wendland function as the interpolation kernel, increased number of neighboring particles and non-reflective open boundary conditions at the outlet of the Venturi tube. The flow structure and differential pressure as well as the mainstream velocity profiles at different stations are compared with calibrated experimental data. A resolution independence test shows that good convergence to the experimental measurements is achieved using four million particles. At this resolution the simulations predict the experimental centerline velocity profile along the Venturi meter for a volumetric flow rate of ten liters per minutes (lpm) with a root-mean-square error of 4.3%. This error grows to 7.1% when the volumetric flow rate increases to 25 lpm. The predicted differential pressure matches the experimental data with errors varying from 1.4% (for 10 lpm) to 6.8% (for 25 lpm). Cross-sectional velocity profiles within the throat and divergent sections differ from the experimental measurements in less than 5.5%. In general, it is shown that the SPH model can provide an efficient and accurate method for recalibrating flow meters at moderately high Reynolds numbers instead of using costly experimental tests.

NUMERICAL SIMULATION SHEAR-THICKENING FLUID THROUGH A SMALL-SCALED HEAT EXCHANGER

This paper aims to predict the behavior of a complex fluid though a small-sized thermal exchanger. The fluid used is of shear-thickening type of power-law index (n = 1.4) and Prandtl number (Pr = 50). The Ostwald model was utilized to define the dynamic viscosity. The exchanger consists of three rectangular cross-section tubes placed inside a thermally insulated chamber. The enclosure contains two ports for the entry and exit of the complex fluid. The complex fluid enters the chamber from the first port at a constant speed and at a low temperature, and then it passes around the hot tubes to be cooled. The rheological behavior of a fluid is defined by Ostwald equation, while the intensity of thermal buoyancy was modeled by Boussinesq approximation. The results showed that the increase of the velocity of the flow at the entrance increases the instability of the flow. Increasing the intensity of thermal buoyancy reduces the cooling process of the hot upper body.

Proppant Transport in a Newtonian Fluid Under Laminar Flow

Summary Model proppant transport experiments are conducted at the laboratory scale using a Newtonian carrier fluid in a long tube of rectangular cross section. Under the particular flow conditions studied, we observe the buildup of a dense but flowing sediment, which rapidly reaches a steady-state height. The existence of this steady-state flowing sediment implies that the proppant flux leaving the channel equals that entering the channel; that is, “efficient” proppant transport occurs. As soon as the suspension flow is stopped, the fluidized sediment ceases flowing and quickly becomes more compact. This collapse implies that the particle sediment is maintained in an expanded state while under flow, with an average volume fraction considerably lower than that under static conditions. The relevant mechanism of sediment transport is identified as viscous resuspension because the flow is at a low Reynolds number (Re at approximately 0.1). We estimate the average volume fraction of the resuspended sediment from experimental measurements of the “expanded” flowing sediment height, with the assumption that the corresponding compact sediment volume fraction is ϕ0=0.61, the volume fraction at which the suspension viscosity diverges. Predictions of the resuspended sediment heights are made with a simple approach based on the diffusive flux model by Leighton and Acrivos (1986) using the average shear stress across the channel width. A good agreement is found between the predicted and experimental values, indicating that 2D effects remain weak. Microscopic observations show that the sediment is fully fluidized while under flow for all the flow rates studied in our channel, and one does not observe the buildup of static sediment banks that are observed in larger-scale tests during the suspension flow (Kern et al. 1959; Babcock et al. 1967; Schols and Visser 1974; Sievert et al. 1981). This apparent difference is explained in the context of the viscous resuspension model.

Improvement of prt-9 constructive system on the basis of frame elements strength balance

Analytical and experimental investigations of the most loaded elements of the base frame of PRT-9 solid organic fertilizer spreader are carried out in this paper. The residual operation life of the central beam of the paired Z-shaped profile, as well as the lateral spars of the Z-shaped cross section are determined. According to the results of studies, it was found that the residual operation life of these system elements differ significantly. In order to achieve strength uniformity of the main frame elements, it is decided to weaken the central beam by replacing the paired Z-shaped profile with a thin-walled tube of rectangular cross-section and strengthen the lateral spars by replacing Z-shaped profile with a channel profile with the same height.

Forming rectangular tubes into complicated 3D shapes by combining three-roll push bending, twisting and rotary draw bending: the role of the fabrication loading history on the mechanical response

Tubular structures find wide application in the automotive context. In particular, rectangular cross-section tubes are used to fabricate structural frames via different techniques, such as Three-Roll-Push-Bending with the addition of twisting component (TRPBT) and the Rotary Draw Bending (RDB). However, whether the accumulated plastic strains, hardening and residual stresses influence the load capacity of the tubular component is still unclear. This paper is intended to shed light on this issue. The load capacity of a tubular mock-up obtained by sequential combination of TRPBT and RDB has been empirically assessed by a destructive compression test. A finite element (FE) model has been devised and validated to analyse the manufacturing processes. This work puts in light the need to correctly model the compliance of the tool set-up for Roll Bending in the numerical calculations. The final shape of the mock-up obtained by FE analysis is the input of the numerical simulation of the compression test. The present modelling has shown clearly that the global resistance of a tubular component is sensitive to plastic strains, hardening and residual stresses resulting from the previous forming processes. Taking into account these three factors greatly improves the capability of the FE to model the mechanical response of the structural part.

Influence of mandrel on the forming quality of bending L-shaped hollow parts

In order to investigate the influence of mandrel on the forming quality of bending L-shaped hollow parts, three types of mandrels, which are polyurethane rubber mandrel, low-melting-point mandrel, and ball bearing mandrel. Polyurethane rubber mandrel and low-melting-point mandrel, which supposed as elastic–plastic deformable part in the numerical simulation. The effect of different forms of mandrel on the forming quality of L-shaped hollow parts, such as section deformation and wall thickness variation, were compared with push bending without a mandrel. The results show that the low-melting-alloy mandrel leads to a better formability and a more uniform tube thickness distribution compared with the polyurethane rubber mandrel and ball bearing mandrel, for the low-point-melting mandrel brings about smaller stress in the bending process. Cold push-bending trials of rectangular cross-section tubes were conducted successfully based on the finite element simulation results. The experimental results showed that the formability and quality of L-shaped tubes greatly improved compared to no mandrel, ball bearing mandrel, and rubber mandrel when the low-melting-point-alloy mandrel was used as the flexible mandrel.

Influence of Impact Location on the Plastic Response and Failure of Rectangular Cross Section Tubes Struck Transversely by a Hemispherical Indenter1

Drop weight impact tests and numerical simulations have been performed to examine the plastic behavior and failure of clamped rectangular cross section tubes subjected to transverse loads. The selected indenter is a hemisphere with diameter of 20 mm. The tube lengths are 125 and 250 mm, and they are struck at the midspan and the quarter-span. The impact point along the width direction is located at the central position and displaced 10 mm from the center, respectively. The results show that the impact location affects strongly the plastic behavior and failure of the tubes. The impact location displaced along the width increases the energy absorbing capability of the tubes accompanied with an asymmetrical deformation mode. The experimentally recorded force–displacement responses and failure modes show good agreement with the numerical simulations, performed by the LS-DYNA finite-element code. The numerical results show the process of crack initiation and propagation and provide the details to analyze the structural plastic deformation and failure of the tubular specimens under transverse loads. The impact characteristics of the rectangular tubes are well presented based on the relevant failure modes observed in beams, plates, and circular tubes. Moreover, the influence of the impact location on the strength of tube specimens is characterized, and the collapse mechanism of rectangular tubes is described.

Modeling duct flow by the R-function method

The article deals with a flow in the tube of rectangular cross-section with an inner circular cylindrical element. We use the numerical method basing on R-functions. This method is meshfree and therefore more efficient than the finite element method that requires remeshing when the geometry of problem is changed. The dependence of the flow on the diameter of the central cylinder and its position in the duct is investigated under constant pressure gradient. It was found that the resistance decreases if the inner element is moved from the center of the duct.

Theoretical, numerical, and experimental study of dynamic axial crushing of thin walled pentagon and cross-shape tubes

Rectangular thin walled tubes are commonly used in front rail structures of automotive chassis, and are designed to absorb maximum amount of energy during frontal impact. With increasing emphasis over the last few decades on building lighter and faster vehicles by auto manufacturers, researchers are actively exploring opportunities to improve crashworthiness of vehicles by exploiting structural and material optimization approaches. In this paper, two new shapes, Pentagon and Cross, were studied for two materials, aluminum and steel, with the objective of improving the crashworthiness of automobiles without adding any additional weight (within the same type of material) to the chassis. The tubes were initially analyzed using finite element method. The performances of proposed tubes were compared with a rectangular cross-section tube by comparing the average mean force (required to crush the tube under 35mph impact velocity) and the total specific energy absorbed. A theoretical plastic analysis was carried out by evaluating the folding mechanisms of tubes for Pentagon and Cross shapes and an analytical model was developed that predicted the mean force necessary to crush the tubes. The numerical and theoretical analysis showed that for equivalent tube wall areas, the aluminum and steel Pentagon and Cross tubes absorbed 31–60% and 48–92% more energy than the rectangular tube. The outputs of proposed predictive theoretical model for the Pentagon and Cross tubes were compared reasonably well with the mean force values calculated through numerical method. An experimental study was conducted on cross tube samples machined from Aluminum AA6061–T6511 blocks with the purpose of validating numerical and theoretical approaches used in the present study. Experimental results for the mean force demonstrated a good correlation with numerical and theoretical approaches with approximately 1% and 6% variation, respectively. In addition, the deformation modes observed in the experiment matches reasonably well with the ones observed in the finite element analysis (FEA) simulations.

Plastic response and failure of rectangular cross-section tubes subjected to transverse quasi-static and low-velocity impact loads

Quasi-static punching tests and dynamic drop weight impact tests have been performed to examine the plastic response and failure of clamped rectangular cross-section tubes struck transversely by a hemispherical indenter. The laboratory results are compared with numerical simulations. The span lengths of the tube specimens are 125 and 250mm, and they are impacted at different locations along the span. The results show that the impact location strongly influences the impact response of the tubes. Since the tubes are fabricated with strain-rate-insensitive high strength steel, the experimental plastic response and failure are similar when the tubes are loaded statically or under low impact velocity. The experimental results are presented in terms of the force–displacement responses and the failure modes, showing a good agreement with the simulations performed by the LS-DYNA finite element solver. The numerical results manage to describe the process of initiation and propagation of the material fracture and provide detailed information to analyse the large inelastic deformation and failure of ship structural components subjected to impact loading. The deformation and failure characteristics of the tube specimens are well described on the basis of the failure modes of the beam and plate models. Moreover, the crack initiation in both upper and lower walls is well described by the matrix of the infinitesimal strain tensors and the deformed shape of the first failing element.

Fully-developed conjugate heat transfer in porous media with uniform heating

We propose a computational method for approximating the heat transfer coefficient of fully-developed flow in porous media. For a representative elementary volume of the porous medium we develop a transport model subject to periodic boundary conditions that describes incompressible fluid flow through a uniformly heated porous solid. The transport model uses a pair of pore-scale energy equations to describe conjugate heat transfer. With this approach, the effect of solid and fluid material properties, such as volumetric heat capacity and thermal conductivity, on the overall heat transfer coefficient can be investigated. To cope with geometrically complex domains we develop a numerical method for solving the transport equations on a Cartesian grid. The computational method provides a means for approximating the heat transfer coefficient of porous media where the heat generated in the solid varies “slowly” with respect to the space and time scales of the developing fluid. We validate the proposed method by computing the Nusselt number for fully developed laminar flow in tubes of rectangular cross section with uniform wall heat flux. Detailed results on the variation of the Nusselt number with system parameters are presented for two structured models of porous media: an inline and a staggered arrangement of square rods. For these configurations a comparison is made with literature on fully-developed flows with isothermal walls.

Optimum design of partially tapered rectangular thin-walled tubes in axial crushing

Straight and tapered thin-walled tubes of rectangular cross-section have been well established as impact energy absorbers under axial loading. This paper investigates the energy absorption capacity and peak transmitted load of partially tapered rectangular tubes. It is shown that these characteristics are notably affected by such design variables as the taper angle and the length of the tapered section. A simulation-based approach is proposed for the fast determination of the optimum geometry of partially tapered tubes. The approach is based on the numerical prediction of the tube's load—deflection response in dynamic loading for various values of design parameters within their respective ranges, followed by a neural net approximation of the finite element (FE) model. The verified neural model would then be used in a multiobjective optimization algorithm that would find Pareto optimal solutions to the design problem. Each solution would be characterized by a non-dominated compromise between maximizing the energy absorption capacity and minimizing the peak impact load.

Thermally Developing Forced Convection and Heat Transfer in Rectangular Plate-Fin Passages Under Uniform Plate Temperature

Laminar forced convection inside plate-fin passages is of interest in the design of a low-Reynolds-number heat exchanger apparatus. Heat transfer to thermally developing, hydrodynamically developed forced convection inside tubes of rectangular cross section with various aspect ratios has been well studied and documented in various books, but for plate-fin ducts there has not been much work done. A typical plate-fin passage is comprised of two horizontal plates and two vertical fins. The main assumption in this study is that the plate is under uniform temperature conditions and the heat fluxes on two fins are distributed in a skew-symmetric manner. Heat conduction in the fin and convection in the fluid are analyzed simultaneously as a conjugate problem. Various duct aspect ratios from 0.125 to 4.0 are considered, and the fins have different conductance parameters from 0 to infinitely large, representing materials from polymers to pure copper. The Nusselt numbers in the developing region, the thermal entry length, and the fully developed values for these passages are obtained, which can be used in estimation of heat transfer performance in plate-fin compact heat exchangers with fins of various thermal conductivities and thicknesses.

Study on varying curvature push-bending technique of rectangular section tube

Abstract This paper presents a new technique of varying curvature push-bending. Different from conventional bending techniques, varying curvature push-bending makes rectangular section tube blank to deform progressively from large radius to small radius in the process of push-bending. The non-uniform curvature of bending die cavity can be defined by the required bending radius and bending tube material. According to actual applied facility, a involute of circle is regard as varying curvature locus equation. The deformation mechanism of rectangular section tube in the push-bending process is analyzed. Smaller curvature radius comparing to minimum bending radius of the tube of rectangular cross-section can be acquired successfully when the being bending angle is given. Corresponding dies have been designed and manufactured so far, and the experiment of varying curvature push-bending has been carried out. Experimental result verifies that it is possible to apply the new process method.

On helicoidal rectangular coordinates for the acoustics of bent and twisted tubes

An oblique, three-dimensional coordinate system called helicoidal rectangular coordinates, is introduced for which the coordinate surfaces coincide with the walls of a tube, with helical centerline and rectangular cross-section. The wave equation in helicoidal rectangular coordinates is solved in terms of sinusoidal functions in time and in the coordinates in the cross-section; the radial dependence is specified by Bessel functions of integer order in the case of a bent and untwisted tube having only curvature of flexion, which contains cylindrical waves. In the case of a bent and twisted tube, with curvature of torsion as well as of flexion, the Bessel functions have real order, not necessarily an integer. The sound fields are determined in the helical tube of rectangular cross-section, including the application of boundary and initial conditions, for waves propagating along the tube and for standing modes trapped between two sections. The application of wall boundary conditions specifies the eigenvalues and eigenfunctions for the modes in the cross-section; the tables of radial wavenumbers and plots of eigenfunctions are given for modes with lowest radial n=1,2,3, azimuthal m=0,1,2 and vertical l=0,1 orders, for several cases: flat and twisted bends, with smaller or larger curvature of flexion and torsion, and square or rectangular cross-sections.

Buckling of thin plates and members — and early work on rectangular tubes

A brief examination of some of the research on the post-buckling elastic and plastic behaviour of plates and plate structures is outlined. This field is so wide ranging that only a very superficial examination of the early research has been carried out, and the writer has concentrated on some specific aspects of the general field of study. A very limited examination of some of the early research on rectangular cross-section tubes is also given.

Frictional drag reduction with air lubricant over a super-water-repellent surface

This paper presents a new technique for reducing frictional drag using a super-water-repellent surface and air-injection (called an SWR & A technique). Its effectiveness was examined by carrying out pressure-loss measurements with a tube of rectangular cross section, along with resistance tests on a horizontal flat plate, a 7.2-m-long tanker model, and a 12-m-long high length-to-beam-ratio model ship. These test results showed that the new technique can significantly reduce the models' frictional drag; for example, the frictional resistance on the SWR surface was reduced by 80% at a speed of 4 m/s and 55% at 8 m/s.

Frictional Drag Reduction with Air Lubricant over Super-Water-Repellent Surface

This paper presents a new technique for reducing frictional drag using a super-water-repellent surface and air-injection (called an SWR & A technique). Its effectiveness was examined by carrying out pressure-loss measurements with a tube of rectangular cross section, along with resistance tests on a horizontal flat plate, a 7.2-m-long tanker model, and a 12-m-long high length-to-beam-ratio model ship. These test results showed that the new technique can significantly reduce the models' frictional drag; for example, the frictional resistance on the SWR surface was reduced by 80% at a speed of 4 m/s and 55% at 8 m/s.

A calculation method for fully developed flows in curved rectangular tubes

In this paper, A method, consisted of perturbation method, Garlerkin method and finite-difference method, is designed to calculate fully developed flows in curved tubes of rectangular cross-section. It costs less computation than that of direct solving N-S equations, and prevents from building high-order difference equations and extra dealing with the boundary conditions. Numerical results in the situation of small curvature and low Dean number is in accordance with former's numerical and experimental results in quality, and it shows the feasibility of this paper's method.

Collapse of square and rectangular tubes in transverse loading

Analysis of the in plane lateral collapse of square and rectangular cross-section tubes is presented by considering the out-of-straightness of horizontal and vertical arms, corner radius, friction between the platens and the deforming specimen and instability of vertical arms. Results of collapse load for tubes of aluminium and mild steel, thus computed, are presented for some typical tube geometrics, and influence thereon of various parameters considered is discussed. Experiments were conducted wherein tubes of square and rectangular cross-sections of both the materials were laterally compressed between two parallel platens in an Instron machine. The observed collapse loads compare very well with the corresponding computed values.