Miter Bend Research Articles

Design sensitivities for scattering-matrix calculation with tetrahedral edge elements

The rates of change of the scattering matrix of a microwave device with respect to geometric or material parameters are of interest to designers, and useful in automatic optimization. They are most efficiently calculated by the adjoint variable method, but this usually entails the additional cost of funding the adjoint solutions. In the finite-element formulation presented here, no new solutions are needed beyond those required to calculate the complete scattering matrix. Explicit expressions are given for the calculation of the required matrix for a tetrahedral edge element. Results are presented for three rectangular waveguide problems: a uniform length terminated in a short-circuit; an H-plane miter bend; and a two-step waveguide impedance transformer.

803 多孔性物質を設置した屈折流路内の伝熱流動に及ぼすグラスホフ数の影響

803 多孔性物質を設置した屈折流路内の伝熱流動に及ぼすグラスホフ数の影響

Effects of a porous medium on local heat transfer and fluid flow in a forced convection field

Abstract A numerical estimation was made for the laminar flow and heat transfer through a porous medium placed in a flow passage with a miter bend. Heat transfer between solid material and fluid was considered in the numerical analysis. The calculations were performed for the Darcy number Da = 1– 2.5× 10−6, the ratio of thermal conductivity of solid material to fluid RRM = 1–1000, the parameter for heat transfer between solid material and fluid Hg = 10–1000 and the Reynolds number Re = 300. The results of local heat transfer and dimensionless stream function were compared for the cases with and without a porous medium. The behavior of the flow, the solid and gas temperatures, the Nusselt number with these parameters and the thermal performance were illustrated. It was found that a porous medium with high RRM and Hg should be selected with an optimum Darcy number to enhance the local heat transfer without a significant flow resistance.

Analysis and design of mitered H-plane bends in rectangular waveguides by combining the mode-matching and port reflection coefficient methods

An accurate and efficient characterization method of mitered H-plane waveguide bends is developed by combining the mode-matching method and the port reflection coefficient method. In the analysis, the two-port waveguide bend is converted to a one-port structure composed of cascaded waveguide step-junctions only. The analysis and computation procedures are greatly simplified thereby. Convergence properties and reliabilities of the obtained numerical results are verified. Variations of the return loss of the mitered bend are investigated with various dimensions of the mitered part. Wide band and low return loss characteristics of the mitered bend are found with the obtained optimal compensation dimension. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 2, 80(5): 1–7, 1997

Effects of upstream pipe fittings on the performance of orifice and conical flowmeters

It is difficult to get high accuracy over a broad measurement range from a flowmeter operating in ideal conditions, but when the device is placed in a hostile environment with highly disturbed flow profiles involving swirl caused by various pipe fittings such as pipe bends installed upstream of metering element, the task becomes even tougher. In this regard, the conical flowmeter seems to fare better than other pressure differential devices. In the present study, experiments were conducted to investigate the effect of upstream pipe fittings such as a single 90° mitre bend, double 90° mitre bends in-plane and double 90° mitre bends out-of-plane on the performance of a conical flowmeter and orifice meter. These measurements are carried out for Reynolds numbers ranging from 30000 to 494000 for a constant β ratio of 0.75 with air as the working medium. Further, static pressure distributions downstream of the orifice meter and conical flowmeter are measured to estimate the irrecoverable pressure drop due to the flowmeter in the line. Results indicate that the conical flowmeter is less sensitive to swirl when compared with the orifice meter. Further, the irrecoverable pressure drop in the conical flowmeter is 50% less than that for the orifice meter.

Mechanical Behavior of Buried Pipeline with a Miter Bend Under internal Water Pressure

Mechanical Behavior of Buried Pipeline with a Miter Bend Under internal Water Pressure

HE11mitre bends and gaps in a circular corrugated waveguide

Abstract The HE11 transmission loss in a mitre bend or gap in a corrugated waveguide is derived using mode matching techniques. For a gap length L in a waveguide of diameter D = 2a at a wavelength λ, the predicted loss for D ⋙ λ is approximately l·7[Lλ(2a2)]3/2dB. Measured data versus gap length oscillate about this predicted value due to the diffraction of very high order modes. For a mitre bend, L = D. The loss in mitre bends where the corrugations are continued up to the mirror should be reduced by half from the above formula due to the reduced diffraction. Measured data on mitre bends that are in agreement with these expectations are presented. In addition, the design of a mitre bend assembly for a 1·25 in waveguide at 110 GHz using an HE11/HE12 mode mixture to reduce the diffraction is described. The measured HE11 transmission losses in six of these assemblies in series were 0·46% and 0·54% per bend for H-plane and E-plane orientations, respectively. The inferred mode conversion loss of 0·38% is less...

Effects of a Porous-Medium in a Forced Convection Field on Local Heat Transfer and Flow.

A numerical estimation was performed for the laminar flow and heat transfer by a porous medium in a flow passage with a miter bend. Heat transfer between solid material and fluid was considered in the numerical analysis. The calculations were performed for the Darcy number Da = 1∼2.5×10-6, the ratio of thermal conductivity of solid material and fluid RRM = 1∼1000, the parameter of heat transfer between solid material and fluid Hg = 10∼1000 and the Reynolds number Re = 300. Local heat transfer and dimensionless stream function were compared between the flow with and without porous medium. The behavior of the flow, the solid and gas temperatures and the Nusselt number with these parameters was represented. It was found that the porous medium with low Da, high RRM and Hg should be selected to enhance the local heat transfer.

An Investigation of the Liquid Petrol Wall Film in the Manifold of a Carburetted Spark Ignition Engine: Effect of Carburettor and Manifold Geometry on Wall Film Quantities, Engine Performance and Emissions

The rate of deposition on the manifold wall of liquid droplets from the multi-component, two-phase stream of fluid flowing in the inlet manifold of a carburetted petrol engine and the re-entrainment of droplets into the stream from the liquid film which flows on the walls have been investigated using a single cylinder crossflow engine. The effect of throttle opening, straight manifold length, a smooth bend and a mitre bend is reported: measurements of exhaust emissions and cycle-to-cycle pressure variation of cylinder pressure are related to wall film quantities. It was found that throttle position was important in determining the initial wall film, that the average thickness of the film decreases with length along the straight manifold and that droplet re-entrainment from a sharp bend is greater than from a smooth bend. Removal of the wall film yields a significant reduction in the emission of unburned hydrocarbons and virtually eliminates cycle-to-cycle variations of pressure in the engine cylinder.

Flexibility Factors and Stress Indices for Piping Components With D/T ≧ 100 Subjected to In-Plane or Out-of-Plane Moment

The finite element analyses are carried out for the several piping components (D/T ≧ 100) subjected to in-plane or out-of-plane moment. For the stress evaluation of the chemical plant piping systems, ANSI B31.3 is usually applied. But the stress intensification factors and flexibility factors in this code are mainly for a heavy-wall-thickness pipe, so it is necessary to reconsider these factors for a thin-wall-thickness pipe with a large diameter. In our study, several finite element analyses using MSC/NASTRAN program were performed on the pipe bends (elbow or miter bend, 0.01 ≦ h ≦ 0.2) and the unreinforced fabricated tees (50 ≦ D/Tr ≦ 300, 0.5 ≦ d/D ≦ 0.95, 0.25 ≦ Tb/Tr ≦ 0.95), and the empirical formulas for the flexibility factors and the stress indices, due to out-of-plane or in-plane moment, were proposed. Experimental stress analyses for the piping components with D/Tr = 127 were also carried out, and it was confirmed that the results agreed well with the numerical ones.

Photoelastic stress analysis in mitred bend under internal pressure.

The stress analysis and stress relaxation in mitred bend subjected to internal pressure have been studied by means of the photoelastic stress freezing method. The experimental results show that stress concentration occurs in the wedge tip of the intersectional plane and it is considerably influenced by the bent angle. Then, the stress relaxation was obtained by planing the wedge tip.

The Design of Mitred Bends—A Background to BS 806 : 1975 Amendment No 3

To satisfy a requirement within the high pressure pipework industry in the UK, PVE/10 of the British Standards Institution established a Working Party to produce recommendations on the design and application of gusseted or mitred bends. The ultimate conclusions of the Working Party were eventually published within Amendment AMD 3545 to BS 806 ‘Ferrous pipes and piping installations for and in connection with land boilers’. Prior to this amendment BS 806 provided only limited guidance on the design of such bends, based on rules derived from custom and practice. AMD 3545 provides more extensive guidance than previously, based on experimental data and analysis and provides guidance on pipework design. This paper describes the background to the amendment and provides most of the reasoning behind the conclusions drawn by the Working Party.

Erosion of a Pipe Bend by Solid Particles Entrained in Water

The erosion process in a 90-deg pipe elbow is studied to determine the magnitude and location of the maximum wear point. A two-dimensional, theoretical model of the erosion process is set up to track the particle trajectories and then calculate the wear at impingement. Erosion tests on electroplated, 1-in. I.D. elbows are made using particle sizes which vary by over an order of magnitude, but the location of maximum wear for an elbow whose R/D value is 1.5 is almost unaffected. The average angle, φ, which locates the point of maximum erosion, is determined to be 85 deg, measured from the beginning of the curve. The average wear coefficient, Ke, is found to be 0.011. Another test using a more gradual bend curvature (R/D = 5.0, and a mitre bend tested as an approximation of an elbow with R/D value of 0.5, give similar results.) There are considerable discrepancies between computed and measured values of the position of maximum wear, because the model does not account for secondary flows. Finally, a simple technique is outlined to predict the erosion depth at the maximum wear point.

Stress Analysis of Mitred Bends by Ring Elements

This paper proposes a ring element for the stress analysis of mitred bends, which is an extension of ring elements for pipe bends proposed by the present authors. Since accurate treatments of continuity conditions on the connecting lines between straight pipe segments are employed and strain-displacement relations derived from the general thin shell theory with shear strains are considered, the present method can be applied to problems of mitred bends of complex configurations under general loading conditions. Shape functions are developed by trigonometric functions and Hermitian polynomials of second order in the circumferential and longitudinal directions, respectively. This finite element method requires fewer number of degrees of freedom for the same accuracy than the conventional shell elements.

Duct acoustics—A numerical technique for the higher order mode solution of three-dimensional problems with rigid walls and no flow

A three-dimensional, time dependent, finite difference technique is developed for the steady state solution of the acoustic wave equation in the absence of flow. The acoustic characteristics of a mitred bend are used to illustrate the use of the technique and numerical results are corroborated by experimental data.

Photoelastic Investigation of the Stresses in Mitred Bent-cylinders Under Bending II : For Various Bent-angles

The states of stress distribution in mitred bend subjected to in-plane uniform bending moment have been studied systematically by means of photoelastic stress freezing method. The relations between the stress concentration factor of fiber stress σl and of hoop stress σθ near the bent art and the angle of mitred bend are thoroughly investigated. The effects of fillet radius of the bent-part and wall thickness on the stress concentration factors are also discussed.

Bend losses in drop inlet spillways

The drop inlet spillway consists of a vertical riser open at the top and connected to a horizontal conduit or tunnel at the bottom. A 90° change in direction is required at the connection between the riser and the conduit. In the interests of simplicity a square bend, sometimes called a miter bend, is often used for small unimportant structures. This type of bend produces separation zones and large eddy losses (bend loss). At the other extreme is the fully curved bend, commonly used for large shaft spillways. A properly designed curved bend will eliminate separation and minimize head loss. However, layout and forming for construction of a curved bend for a tunnel is complicated and expensive because the elbow surface is of double curvature.In this paper the results of hydraulic tests on five bend designs are presented. It was found that a simplified design with only an inside curve performed almost as well as the fully curved bend. It is suggested that the proposed design will meet the requirement for many low head drop inlets where use of the fully curved bend is not warranted but the square bend is not satisfactory.

Duct acoustics—A time dependent difference approach for steady state solutions

A time dependent numerical technique is developed to study the propagation of sound in ducts in the absence of flow. The method is shown to be stable and convergent for propagating and decaying modes. Sample calculations are compared with analytical solutions in straight ducts and with numerical and experimental results in a mitred bend.

Cavitation Performance of Miter Bends : Part 2-Effect of Spacing between Bending Points of Two-fold Miter Bend

Cavitation Performance of Miter Bends : Part 2-Effect of Spacing between Bending Points of Two-fold Miter Bend

Transmission and reflection of higher order acoustic modes in a mitred duct bend

A two dimensional finite element technique was used to investigate the characteristics of a 90° mitred bend for higher order modes. Experiments were used to corroborate the numerical results and good agreement was obtained between the two approaches for values of the wave number parameter extending to a little above the cut-on value of the second cross mode. The results are presented as modal contributions of the reflected and transmitted sounds when a propagating mode is incident on the bend. The magnitude of the energy transfer is also examined for the case where an evanescent mode is incident on the bend.