Noncircular Section Research Articles

Design method for circular and non-circular sewer sections

An analytical method is presented for the determination of hydraulic and geometric elements of partly full flowing circular and non-circular sections with known parameters being discharge, depth of flow, bed slope and Manning's roughness coefficient. This method will eliminate the application of tabular and graphical form of hydraulic elements for partly full flow conditions, which provide relationships between partly full flow and full flow hydraulic and geometric parameters for sewer system design. The method can also be applied to stormwater system design and is extendable to any shape of sewer or stormwater pipe cross sections.

Investigation of Tunnel Stress Path During Face Advancement

AbstractTunnel stress path during excavation was investigated in the study scope. The triple-center section is commonly designated for highway tunnels, but the analytical solution of the stress state for a non-circular tunnel section with multiple bench excavations is difficult to obtain. Our investigation provides an algorithmic procedure which reliably evaluates stress adjustment of a bench excavation with respect to the three-dimensional state of stress. Evaluation of a safety factor at the tunnel face during advancement is performed following the stress path and principal stress space.

Hydraulic assessment of non-circular-section building drainage

The development of non-circular cross-section in-building drains with a reduced invert cross-section will allow efficient low-flow performance by maintaining flow depth to aid solid transport. An enlarged upper cross-section will allow higher water and air flow rates to be handled. Such developments are essential if the water-conservation benefits of a reduced toilet flush volume are to be realized. The paper demonstrates the background to such solutions based on the ovoid or ‘egg-shaped’ cross-section sewers that have been used in Europe and the US for two centuries. The steady flow capacity of the ovoid shape is demonstrated, while the reduced wave attenuation in ovoid cross-sections is simulated, using the method of characteristics solution to the wave equations, and it is shown to be an indicator of improved overall solid transport efficiency. Solid transport results demonstrate the efficiency of non-circular sections and provide a direct comparison with the use of reduced-diameter circular drains already acceptable in conjunction with reduced water usage. Le développement de collecteurs d'immeubles avec coupe transversale non circulaire et coupe transversale de radier réduite permettra d'obtenir de bonnes performances en faible écoulement en maintenant la profondeur de l'écoulement pour faciliter le transport des matières solides. Une coupe transversale supérieure agrandie permettra d'accepter des débits d'eau et d'air plus élevés. De telles évolutions sont indispensables si l'on veut profiter des avantages apportés par la réduction du volume des eaux de chasse et ainsi préserver l'eau. Cet article expose l'origine de telles solutions basées sur la coupe transversale ovoïde des égouts que l'on trouve en Europe et aux États-Unis depuis deux siècles. La capacité d'écoulement constant de la forme ovoïde est démontrée alors que l'atténuation de l'onde réduite dans les coupes transversales ovoïdes est simulée, en utilisant la méthode de la solution caractéristique appliquée aux équations d'ondes; on démontre qu'il s'agit d'un indicateur d'efficacité globale améliorée du transport de matières solides. Les résultats concernant le transport de matières solides démontrent l'efficacité des sections non circulaires et fournissent une comparaison directe avec l'utilisation de collecteurs circulaires de diamètre réduit déjà acceptables dans le contexte de la réduction de l'utilisation de l'eau. Mots-clés: Services pour les bâtiments, conception des égouts, système d'égouts, section ovoïde, transport de matières solides, préservation de l'eau, atténuation de l'onde

Analytical modeling of wall thinning during corner filling in structural tube hydroforming

In a tube hydroforming process, an internal pressure is used to expand a circular tube into one with non-circular sections. Friction at the material/die interface plays an important role in determining the distribution of the thickness during deformation. In this paper, an analytical model is developed to determine the variation in the stresses and strains along the tube wall as the internal pressure increases to expand the circular tube into a square cross-section. Based on the analytical model, a parametric study is conducted on the effects of the coefficient of friction and the material properties on the distribution of cross-section thickness in the hydroformed tubes. Such parametric study is useful in establishing guidelines for designing the structural tube hydroforming process. It also helps in the search for limits of the process capabilities. One of the strengths of analytical modeling is that it gives more insights into the mechanism through which friction affects the deformation during tube hydroforming.

Design Method and Numerical Control Machining Principle for an Arbitrary n-polygon Noncircular Section

By analyzing the structure characteristics of arbitrary n-polygon noncircular sections, mathematical formulas among the characteristic parameters were set up, and a theorem for designing this kind of sections was deduced by mathematical induction method. Based on the mechanistic transmission principle, the control theorems for the numerical control (NC) grinding of arbitrary n-polygon noncircular sections and the control model for the multicoordinate motion were built. A feed rate self-adjusting method was proposed to uniform the grinding speed with the changes of sectional curvature. Then, an NC machine tool for grinding n-polygon noncircular sections was developed. The test results of the grinded parts showed that the section profiles accorded with the design demands: the roughness was less than 0.32 μm and the dimensional accuracy was within 8 μm. The results prove that the proposed theorems and method can effectively direct the design and manufacture of the polygonal noncircular connection.

Analytical approach to noncircular section birdcage coil design: Verification with a Cassinian oval coil

A general analytical framework is presented for the design of birdcage radiofrequency resonators on cylindrical formers having arbitrary cross-sectional shape. The primary objective of such shapes would be to improve the sensitivity of the NMR experiment to noncircular regions of the human anatomy while maintaining field homogeneity and quadrature polarization comparable to those of standard circular birdcage coils. The shape of the corresponding radiofrequency screen, which is required to decouple the coil from the rest of the NMR system and which is key to the performance, is also provided by this methodology. The theory was tested by constructing a 3-T, quadrature, proton coil on a shape conforming to the anthropomorphic mean of the human head, namely, the oval of Cassini. Both bench tests (Q) and in vivo spectral and imaging comparisons of the Cassinian coil with an equivalently dimensioned and constructed circular birdcage coil, respectively, predicted and demonstrated in vivo an improvement in SNR of approximately 24% over the circular section coil. The experimental RF field homogeneity and quadrature performance were comparable for both coil geometries, with the circular coil being marginally superior.

Modelling of Accelerated Pipe Freezing

The use of pipe freezing as an advanced maintenance technique and the potential advantages of freezing non-circular sections were highlighted in an earlier paper. This work reports in detail on the finite element modelling of the freeze in a non-circular section. The formulation and operation of the model is explained and predicted time-to-freeze compared with the results of new experiments.

Single-mode, single-polarization VCSELs via elliptical surface etching: experiments and theory

Polarization control in vertical-cavity surface-emitting lasers (VCSELs) has attracted a lot of interest and different techniques have been proposed to achieve it. Among them, one of the most attractive relies on slight modifications of existing and well-behaving devices, i.e., by introducing a noncircular transverse section layer somewhere in the device. Even though experimental verifications of this principle have already been carried out, a theoretical framework to better understand and possibly optimize such devices is still missing. This mainly originates from the need of a fully vectorial and three-dimensional approach. In this paper, we will undertake a joint experimental and theoretical effort: first, we give experimental evidence of polarization control by applying elliptical surface etching. Then, after having validated the vectorial electromagnetic model by comparing numerical and experimental results, we are able for the first time to explain and compare the polarization selection mechanisms and, consequently, to provide guidelines for optimized structures.

Accelerated Pipe Freezing in Non-Circular Sections

Pipe freezing is increasingly used in a range of industries to solve otherwise intractable pipe line maintenance and servicing problems. There is, however, a limit to the size of circular pipe that may be plugged using the technique. Ice, and most other fluids encountered in their frozen state, are poor thermal conductors that tend to insulate the fluid remaining in the core. For large diameters a closed plug cannot be formed no matter how much cooling is applied at the outer surface. Experiments have been conducted to investigate the advantages of freezing non-circular sections. It is shown that by reducing the distance between the fluid and cooled wall whilst at the same time maintaining the flow area of the pipe there is no limit to the nominal size of line that may be plugged by freezing. Significant advantages are gained when freezing all sizes of pipe. Strategically placed non-circular sections can eliminate the need for conventional valves and might find wide application in the hydrocarbon, utility and building services industries.

Conceptual Design Principles for Non-Circular Pressurized Sandwich Fuselage Sections – a Design Study Based on a High-Order Sandwich Theory Formulation

Results obtained as part of a design study regarding a non-circular pressurized sandwich fuselage section are presented. The originating problem is associated with preliminary studies for the “Global Range Transport” envisaged by the “New World Vistas” program of the United States Air Force. The modeling and analysis is conducted usinga high-order sandwich theory formulation in which the elastic response of each face laminate is accounted for, includingbending-stretching couplingand transverse shear deformations, and where the transverse flexibility of the core is included. The sandwich fuselage envisaged may contain flat, tapered and curved sandwich elements, and a high-order sandwich theory formulation is developed to analyze each of these configurations. The paper includes a presentation of the adopted high-order sandwich theory with special emphasis on the application for the analysis of sandwich panels with variable core thickness, and for the analysis of curved sandwich panels. Numerical results obtained for two different mid-plane asymmetric fuselage sections are presented and compared; one with constant core thickness, and one with varyingcore thickness.

Conceptual Design Principles for Non-Circular Pressurized Sandwich Fuselage Sections -- A Design Study Based on a High-Order Sandwich Theory Formulation

Results obtained as part of a design study regarding a non-circular pressurized sandwich fuselage section are presented. The originating problem is associated with preliminary studies for the “Global Range Transport” envisaged by the “New World Vistas” program of the United States Air Force. The modeling and analysis is conducted usinga high-order sandwich theory formulation in which the elastic response of each face laminate is accounted for, includingbending-stretching couplingand transverse shear deformations, and where the transverse flexibility of the core is included. The sandwich fuselage envisaged may contain flat, tapered and curved sandwich elements, and a high-order sandwich theory formulation is developed to analyze each of these configurations. The paper includes a presentation of the adopted high-order sandwich theory with special emphasis on the application for the analysis of sandwich panels with variable core thickness, and for the analysis of curved sandwich panels. Numerical results obtained for two different mid-plane asymmetric fuselage sections are presented and compared; one with constant core thickness, and one with varyingcore thickness.

Confinement evaluation of concrete-filled box-shaped steel columns

This paper presents a three-dimensional finite element analysis methodology for a quantitative evaluation of confinement in concrete-filled box-shaped unstiffened steel columns. The confinement effects of concrete in non-circular sections can be assessed in terms of maximum average lateral pressure. A brief review of a previous method adopted for the same purpose is also presented. The previous method is based on a two-dimensional finite element analysis method involving a concrete-steel interaction model. In both the present and previous methods, average lateral pressure on concrete is computed by means of the interaction forces present at the concrete-steel interface. Subsequently, the strength enhancement of confined concrete is empirically related to the maximum average lateral pressure. The results of the former and latter methods are then compared. It is found that the results of both methods are compatible in terms of confined concrete strengths, although the interaction model yields a somewhat overestimated estimation of confinement than those of the present method when relatively high strength concrete is used. Furthermore, the confinement in rectangular-shaped sections is investigated and the reliability of previously adopted simplifications in such cases is discussed.

A study on swirling flows in a rectangular channel (LDV measurement, flow visualization and large eddy simulation)

The purpose of this study is to make clear the behavior of swirling pipe flows with non-circular section. We have investigated experimentally and numerically the swirling flows in a rectangular channel with aspect ratio of 1.3, which is one of the typical pipe flow with non-circular section. In this paper, experimental apparatus with water circulation system is produced, and LDV measurement of the swirling flows is performed in order to clarify the mean velocities and turbulent quantity with higher accuracy. In addition, flow visualization for movement of vortex core region in the swirling flows is carried out using tracer method. Moreover, large eddy simulation (LES) of the flow field is made and compared with the experimental results. As results of these investigations, the behavior of the swirling flows in the rectangular channel is totally discussed.

Research on the on-line measuring system for the middle-convex and varying ellipse piston skirt

The middle-convex and varying ellipse piston is th e key component of an internal-combustion engine. In general,the piston is mac hined by non-circular section CNC lathe,but the measuring of piston profile is manipulated by off-line. Because the off-line measuring reference is differen t from the machining reference,the measurement result is diverse from the act ual dimension. A new method to measure the middle-convex and varying ellipse p iston profile, which is known as on-line measuring, is presented. By using thi s kind of method,the high measurement accuracy can be gained,as well as meeting the production requirement.

Spreadsheet Applications for Modelling and Analysis in Mechanical Engineering

This paper outlines a number of different applications of spreadsheet solutions to mechanical engineering problems involving ideal fluid flow, two-dimensional heat transfer, plate bending and torsion of non-circular sections. The general utility of a spreadsheet in handling finite difference equations is further illustrated in an application to simulate the dynamic response of a DC voltage controlled servo-motor. Finally, since most spreadsheets also incorporate the common logical operators then any arbitrary Boolean function can be manipulated with any range of input logic states. Details are therefore included in the paper on the application of a spreadsheet to simulate and test the operation of a prototype digital logic circuit. The educational advantages in using a spreadsheet are highlighted in the variety of engineering problems which can be solved without having to resort to the specialist and generally more expensive finite element software packages.

Estimating Volume Flow Rates Through Xylem Conduits

We discuss the errors in common approximations of the volume flow rate for laminar flow through conduits with noncircular transverse sections. Before calculating flow rates, ideal geometric shapes are chosen to represent the noncircular transverse sections. The Hagen–Poiseuille equation used with hydraulic diameter underestimates the volume flow rate for laminar flow through conduits even with such ideal shapes. Correction factors that have been proposed for the Hagen–Poiseuille equation also lead to underestimates of the volume flow rate for those shapes. The exact solutions are sometimes difficult to attain, but rates calculated using the exact solutions for the ideal shapes may be as much as five times higher than the approximated rates for common transversely elongated shapes. Either the exact solutions or the approximations may be used to calculate volume flow rates through the xylem of plants. Both of these methods actually approximate flow through the original conduits because the shapes used are approximations of the conduits’ transverse sections. We recommend using the exact solutions whenever possible; they should be closer to the real solution than other approximations. We give tables of correction factors for use in the cases where calculating volume flow rate from the approximate solution, the Hagen–Poiseuille equation, is more feasible. Obtaining theoretical volume flow rates that are larger than previously thought highlights the need to clarify the causes of differences between the theoretical rates and the smaller measured volume flow rates in plant xylem.

Estimating volume flow rates through xylem conduits

We discuss the errors in common approximations of the volume flow rate for laminar flow through conduits with noncircular transverse sections. Before calculating flow rates, ideal geometric shapes are chosen to represent the noncircular transverse sections. The Hagen–Poiseuille equation used with hydraulic diameter underestimates the volume flow rate for laminar flow through conduits even with such ideal shapes. Correction factors that have been proposed for the Hagen–Poiseuille equation also lead to underestimates of the volume flow rate for those shapes. The exact solutions are sometimes difficult to attain, but rates calculated using the exact solutions for the ideal shapes may be as much as five times higher than the approximated rates for common transversely elongated shapes. Either the exact solutions or the approximations may be used to calculate volume flow rates through the xylem of plants. Both of these methods actually approximate flow through the original conduits because the shapes used are approximations of the conduits’ transverse sections. We recommend using the exact solutions whenever possible; they should be closer to the real solution than other approximations. We give tables of correction factors for use in the cases where calculating volume flow rate from the approximate solution, the Hagen–Poiseuille equation, is more feasible. Obtaining theoretical volume flow rates that are larger than previously thought highlights the need to clarify the causes of differences between the theoretical rates and the smaller measured volume flow rates in plant xylem.

Ribbon phases in surfactant systems Comparisons between experimental results and predictions of a theoretical model

Abstract Ribbon phases consist of long cylindrical aggregates that have non-circular normal sections. We have recently pointed out that scattering data for a large number of different intermediate ribbon phases of lower than hexagonal symmetry found in ionic surfactant systems indicate that these phases have a structure possessing a centred rectangular symmetry. In this communication, we have investigated the aggregate dimensions for the phases with cylindrical aggregates, i.e., the hexagonal phases and the centred rectangular ribbon phases. Previously published phase diagrams, small angle X-ray and neutron scattering data and 2HNMR data for these phases in different systems have been used for this purpose. The results are that the axial ratios of the aggregates increase when the temperature decreases, when the surfactant concentration increases, and when the average surfactant charge decreases. Models that semi-quantitatively describe the thermodynamics of the micellar, hexagonal and lamellar phases, which are based on the Poisson–Boltzmann cell model approach, have previously been presented in the literature. We have extended these models to treat also the ribbon phases. The results from the calculations show the same trends with respect to changes in the dimensions of the non-circular aggregates upon changes in temperature, surfactant concentration and average surfactant charge, as those obtained experimentally. Theoretically calculated phase diagrams with ribbon phases are also presented. Based on the predictions of the model and some previously published experimental data for hexagonal phases, it is proposed that the formation of non-circular, cylindrical aggregates is a general property of single-chain, ionic surfactant/water systems, and that these aggregates in general pack on hexagonal lattices. The normal sections of these aggregates are circular on average, on account of the fact that the degree of deformation and the orientation of deformation changes along the axis of the aggregates and with time. Only for some systems, temperatures and surfactant concentrations do the asymmetric aggregates line up and ribbon phases with centred rectangular symmetry are obtained. The driving mechanisms for the transition from the hexagonal phase with asymmetric (fluctuating) cylinders and further to the centred rectangular phase with asymmetric (stiff) cylinders is also discussed. It is argued that this phase transition is of the first order.

Applied fluid mechanics

Applied fluid mechanics

Finite element analysis of steady-state three-dimensional helical extrusion of twisted sections using recurrent boundary conditions

In metal-forming, there are problems with recurrent shapes and without explicitly prescribed boundary conditions. In such problems, so-called recurrent boundary conditions must be introduced. The present study is concerned with three-dimensional finite element analysis for helical extrusion of twisted sections. A finite element analysis is carried out for steady-state three-dimensional helical extrusion of noncircular twisted sections, such as clover and trocoidal gear sections, through curved dies. The curved die profiles are described by continuous functions by which smooth transitions of the die surface from the entrance to the exit are obtained. The work-hardening effect is considered by integrating the effective strain rate along each stream line through interpolation by the least-square method. The computed extrusion pressures by the finite element method are compared with the experimental results. The extrusion pressure, as well as the twist angle of working material, is compared for several friction factors. Distorted flow patterns in the three-dimensional space and the distribution of the final effective strain are also obtained.