A comparison of plastic collapse and limit loads for single mitred pipe bends under in-plane bending

This paper presents a comparison of the plastic collapse loads from experimental in-plane bending tests on three 90° single un-reinforced mitred pipe bends, with the results from various 3D solid finite element models. The bending load applied reduced the bend angle and in turn, the resulting cross-sectional ovalisation led to a recognised weakening mechanism. In addition, at maximum load there was a reversal in stiffness, characteristic of buckling. This reversal in stiffness was accompanied by significant ovalisation and plasticity at the mitre intersection. Both the weakening mechanism and the post-buckling behaviour are only observable by testing or by including large displacement effects in the plastic finite element solution. A small displacement limit solution with an elastic-perfectly plastic material model overestimated the collapse load by more than 40% and could not reproduce the buckling behaviour.     

Shakedown and limit analysis of 90° pipe bends under internal pressure,cyclic in-plane bending and cyclic thermal loading

The Linear Matching Method is used to create the shakedown limit and limit load interaction curves of 90° pipe bends for a range of bend factors. Two load cases are considered i) internal pressure and in-plane bending (which includes opening, closing and reversed bending) and ii) internal pressure and a cyclic through wall temperature difference giving rise to thermal stresses. The effects of the ratios of bend radius to pipe mean radius (R/r) and mean radius to wall thickness (r/t) on the limit load and shakedown behaviour are presented.     

A review of literature for the structural assessment of mitred bends

This paper presents a state-of-the-art review of literature available for the structural assessment of all types of mitred pipe bends. Compared with smooth bends, the volume of literature available for mitres is less extensive and its scope is not as wide. Historically, this reflects a reduced application level, as well as a less demanding range of applications, such as non-high temperature use. There is also the issue that an analysis of a mitred bend is complicated by discontinuity stresses, as well as those due to cross-section ovalisation. This fact delayed the development of non-linear analysis of mitred bends. Nevertheless, there is now a substantial body of work on mitred bends. This review tabulates and characterises all publications to date in chronological order. The details of experimental specimens are highlighted, with a view to these perhaps providing useful verification data for any future finite element analysis for example. Issues of particular interest to pipework designers are discussed, including the effects of combinations of loading, out-of-circularity, tangent pipe length and flanges. Failure characteristics and loads are discussed where relevant. Topics for further research are also noted. For example, comprehensive design curves do not exist for the elastic and plastic behaviour of all mitre types, over a practical range of geometry and loading parameters. Similarly, there is still scope for further work on the effect of combined loading, end effects and out-of-circularity. Limit, collapse and burst loads are not yet available across the entire spectrum of bends and loading parameters either. Creep and optimisation represent virgin territory as far as mitred bends are concerned and given that unforeseen vibration is a common source of high-cycle fatigue failure in pipework, there must also be scope for vibration-induced fatigue studies.     

Effects of attached straight pipes on finite element limit analysis for pipe bends

The effect of the length of an attached straight pipe on the plastic limit load of a 90° pipe bend under combined pressure and bending is quantified, based on finite element (FE) limit analyses using elastic–perfectly plastic materials with the small geometry change option. Systematic FE limit analyses of pipe bends with various lengths of the attached pipe are performed. It is shown that the effect of the length of the attached straight pipe on plastic limit loads can be significant, and the limit loads tend to decrease with decrease of the length of the attached straight pipe. In the limiting case of no attachment, the limit loads are found to be close to existing analytical solutions.     

Limit loads for pipe bends under combined pressure and in-plane bending based on finite element limit analysis

Approximate plastic limit load solutions for pipe bends under combined internal pressure and bending are obtained from detailed three-dimensional (3-D) FE limit analyses based on elastic-perfectly plastic materials with the small geometry change option. The FE results show that existing limit load solutions for pipe bends are lower bounds but can be very different from the present FE results in some cases, particularly for bending. Accordingly closed-form approximations are proposed for pipe bends under combined pressure and in-plane bending based on the FE results.     

Dependence of critical radius of the cubic perovskite ABO3 oxides on the radius of A- and B-site cations

Critical radius (r_C) for cubic perovskite structure is an important factor affecting the migration energy of oxygen ions. The monotonic dependence of the critical radius on the ionic radii of A- and B-site cations in cubic perovskite ABO₃ structure was systematically investigated by strict mathematical derivation. When the tolerance factor (t) < 1, the critical radius is a decreasing function but an increasing function with respect to the radius of A-site cation (r_A) and B-site cation (r_B), respectively. For the case of t > 1, there is a reverse dependence of r_C on r_A and r_B. With respect to the case of t = 1, r_C displays a decreasing function with respect to both r_A and r_B.     

A two-stage Lie-group shooting method (TSLGSM) to identify time-dependent thermal diffusivity

We consider an inverse problem for identifying a time-dependent thermal diffusivity α(t) in a heat conduction equation T_t(x, t) = α(t)T_xx(x, t), with the aid of an extra measurement of temperature at an internal point of a rod. Because the data are acquired at an inner point we require to develop a two-stage Lie-group shooting method (TSLGSM) to solve this inverse problem. The present approach is novel and is examined through some numerical tests. By comparing the calculated results with exact ones we can assure that the TSLGSM is an accurate and efficient method, whose estimation error is small even for the identification of a discontinuous and oscillatory thermal diffusivity. Under noise, the identified solutions are also acceptable.     

Limit loads for piping branch junctions under internal pressure and in-plane bending—Extended solutions

The authors have previously proposed plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on finite element (FE) limit loads resulting from three-dimensional (3-D) FE limit analyses using elastic–perfectly plastic materials [Kim YJ, Lee KH, Park CY. Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending. Int J Press Vessels Piping 2006;83:645–53]. The solutions are valid for ratios of the branch-to-run pipe radius and thickness from 0.4 to 1.0, and for the mean radius-to-thickness ratio of the run pipe from 10.0 to 20.0. Moreover, the solutions considered the case of in-plane bending only on the branch pipe. This paper extends the previous solutions in two aspects. Firstly, plastic limit load solutions are given also for in-plane bending on the run pipe. Secondly, the validity of the proposed solutions is extended to ratios of the branch-to-run pipe radius and thickness from 0.0 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 5.0 to 20.0. Comparisons with FE results show good agreement.     

Parametric survey of upper and lower bound limit internal pressures for single mitred pipe bends of various geometries

Internal pressure limit analysis for cylinder–cylinder intersections forming various geometries of single mitred pipe bends subject to internal pressure was investigated. Lower bound analysis with new formulations of force and moment equilibrium together with a higher number of parameters were utilized which resulted in better stability compared to a previously similar analysis of the same problem. Simultaneously, ABAQUS finite element plastic collapse internal pressures were obtained as upper bounds to this problem. Two sets of results were compared, showing good agreement with each other at most points. However, a discrepancy at a mitre angle of 45 degrees between the two sets of results could not be successfully explained. Apart from the conflicting internal limit pressure at the mitre angle of 45°, it is strongly concluded that the true limit internal pressures are bounded between the two sets of results.     

Asymptotic integration of nonoscillatory differential equations: a unified approach

We consider the equation [r(t)x′]′ + f(t)x = 0 as a perturbation of the equation [r(t)y′]′ + g(t)y = 0, where the latter is assumed to be nonoscillatory at infinity. The functions r and g are real-valued, r is positive, and f is complex-valued. The problem of the asymptotic integration of the perturbed equation in comparison with solutions of the unperturbed equation has been studied by many mathematicians, including Hartman and Wintner, Trench, ˇSimˇsa, Chen, and Chernyavskaya and Shuster. Here we apply a unified approach. Working in a matrix setting, we use preliminary and so-called conditioning transformations to bring the system in the form [(z)\vec] = [ L (t) + R(t) ][(z)\vec] \vec{z} = \left[ {\Lambda (t) + R(t)} \right]\vec{z} , where Λ is a certain diagonal matrix and R is an absolutely integrable perturbation. This allows us to use Levinson’s fundamental theorem to find the asymptotic behavior of solutions and, in addition, to estimate the error involved. This method allows us to derive these known results in a more unified setting and to weaken the hypotheses in some instances.     

Parametric survey of upper and lower bound limit in-plane bending moments for single mitred pipe bends of various geometries

The problem of limit analysis for a cylinder–cylinder intersection forming a single mitred pipe bend subject to in-plane bending has been investigated. Lower bound analysis with new equations of force and moment equilibrium together with a higher number of parameters resulted in more stability as compared to a previous analysis of the same problem [PhD Thesis, The University of Manchester, 1991]. Concurrently, abaqus finite element plastic collapse moments were obtained as upper bounds to the problem. Two sets of results were compared, showing good agreement with each other. It could be finally concluded that the true limit moments are bounded in between.     

Co-design and aerodynamic study on a two-step high pressure reducing system for hydrogen decompression: From hydrogen refueling station to hydrogen fuel cell vehicle

Fuel for hydrogen fuel cell vehicles comes from hydrogen refueling stations. During the hydrogen filling process, a high-pressure gradient from 35 MPa (hydrogen storage pressure) to 0.16 MPa (fuel cell pressure) is generated. Such a large pressure gradient posed a challenge to the design of the pressure reducing system. Traditional system is difficult to reduce hydrogen pressure from 35 MPa to 0.16 MPa without accompanying large noise and energy consumption. This work is exploring a new concept to combine the multi-stage continuous resistance perforated components and the Tesla valve to design a two-step high pressure reducing system for hydrogen decompression. To validate the superiority of the developed system, a detailed aerodynamic study on the new system is performed, since aerodynamic performance directly affects the operating flexibility and stability. Finally, the optimized co-design of the system is achieved. Results show that the new system is well-designed for hydrogen decompression with the function of control noise and energy consumption. Larger orifice radius (r₁/r₀) and orifice ratio (k) contribute the better aerodynamic performance. Angle α = 45° is considered the best for better aerodynamic performance. The descending order of the effects on better aerodynamic performance is angle (α), row (m), sleeve stage (N), orifice radius (r₁/r₀) and width (t₁/t₀). This study provides basic support for experts to achieve throttling design of related pressure control systems in hydrogen industry.     

Limit loads for thin-walled piping branch junctions under internal pressure and in-plane bending

The present work presents plastic limit load solutions for thin-walled branch junctions under internal pressure and in-plane bending, based on detailed three-dimensional (3-D) finite element (FE) limit analyses using elastic–perfectly plastic materials. To assure reliability of the FE limit loads, modelling issues are addressed first, such as the effect of kinematic boundary conditions and branch junction geometries on the FE limit loads. Then the FE limit loads for branch junctions under internal pressure and in-plane bending are compared with existing limit load solutions, and new limit load solutions, improving the accuracy, are proposed based on the FE results. The proposed solutions are valid for ratios of the branch-to-run pipe radius and thickness from 0.4 to 1.0, and the mean radius-to-thickness ratio of the run pipe from 10.0 to 20.0.     

Heat transfer and friction factor correlations of solar air heater ducts artificially roughened with discrete V-down ribs

The heat and fluid flow characteristics of rectangular duct having its one broad wall heated and roughened with periodic ‘discrete V-down rib’ are experimentally investigated. Reynolds number (Re) has been varied from 3000-15000 with relative gap width (g/e) and relative gap position (d/w) range of 0.5-2.0 and 0.20-0.80 respectively. The respective variation in relative roughness pitch (P/e), angle of attack (α) and relative roughness height (e/D_h) have been 4-12, 30°-75° and 0.015-0.043. The effect of roughness parameters on Nusselt number (Nu) and friction factor (f) has been determined and the results obtained were compared with those of smooth duct. The maximum increase in Nu and f over that of smooth duct was 3.04 and 3.11 folds respectively. The rib parameters corresponding to maximum increase in Nu and f were d/w = 0.65, g/e = 1.0, P/e = 8.0, α = 60° and e/D_h = 0.043. Correlations for the Nu and f in terms of Re and rib parameters have been developed.     

A self-adaptive LGSM to recover initial condition or heat source of one-dimensional heat conduction equation by using only minimal boundary thermal data

The present study is concerned with the recovery of an unknown initial condition for a one-dimensional heat conduction equation by using only the usual two boundary conditions of the direct problem for heat equation. The algorithm assumes a function for the unknown initial condition and derives an inverse problem for estimating a spatially-dependent heat source F(x) in T_t(x, t) = T_xx(x, t) + F(x). A self-adaptive Lie-group shooting method, namely a Lie-group adaptive method (LGAM), is developed to find F(x), and then by integrations or by solving a linear system we can extract the information for unknown initial condition. The new method possesses twofold advantages in that no a priori information of unknown functions is required and no extra data are needed. The accuracy and efficiency of present method are confirmed by comparing the estimated results with some exact solutions.     

Plastic collapse of pipe bends under combined internal pressure and in-plane bending

Plastic collapse of pipe bends with attached straight pipes under combined internal pressure and in-plane closing moment is investigated by elastic–plastic finite element analysis. Three load histories are investigated, proportional loading, sequential pressure–moment loading and sequential moment–pressure loading. Three categories of ductile failure load are defined: limit load, plastic load (with associated criteria of collapse) and instability loads. The results show that theoretical limit analysis is not conservative for all the load combinations considered. The calculated plastic load is dependent on the plastic collapse criteria used. The plastic instability load gives an objective measure of failure and accounts for the effects of large deformations. The proportional and pressure–moment load cases exhibit significant geometric strengthening, whereas the moment–pressure load case exhibits significant geometric weakening.     

Evaluating the optimum load range for box-type solar cookers

This paper introduces a new concept of Optimum Load Range (OLR) for solar cookers. OLR gives the load values for which cooker preferably shows good thermal as well as good cooking performance; it may be considered a crucial parameter for solar cookers. This OLR concept is based on the dependence of rate of rise of load temperature on different heat transfer processes between load and cooker interior. This concept illustrates solar cooking in two simple steps. The total time required to complete these steps puts an essential constraint for cooking of any load amount. The maximum value of load (upper limit of OLR) till which cooker shows satisfactory cooking may be determined from this constraint. This constraint requires determination of two OLR parameters which are t_{step I} and t_{step II}. The load for which cooker remain almost 30% efficient, may be referred as lower limit (minimum value) of OLR. For the verification of OLR, experimental studies have been conducted with a solar cooker named SFSC. The OLR parameters along with different thermal performance parameters (TPPs) (second figure of merit (F₂), utilization efficiency (η_u) etc.) suggested by different researches for solar cookers in water load condition have been computed from the measured thermal profiles of different loads (0.8–3.0 kg). From the curve analysis of different TPPs with load, the existence of upper limit of OLR is observed. The values of rate of rise of load temperature at water temperatures 80, 85 and 90 °C for different loads also confirm the same. The OLR of SFSC is found to be 1.2–1.6 kg.     

The computed characteristics of turbulent flow and convection in concentric circular annuli. Part II. Uniform heating on the inner surface

Exact numerical solutions, essentially free of empiricism were obtained for fully developed turbulent forced convention in concentric circular annuli with uniform heating on the inner wall and no heat transfer the through the outer wall. The numerically computed values of Nu are represented almost exactly as a function of Nu₀, Nu₁, Nu_∞, and Pr_t/Pr. Here, Nu₀ and Nu_∞ are the limiting and asymptotic solutions for Pr = 0 and Pr → ∞ respectively, and Nu₁ is the special solution for Pr = Pr_t ≈ 0.8673. The predicted values for all Re, all Pr, and all aspect ratios are in agreement with the experimental data within their scatter.     

Experimental and numerical investigations of aerodynamic loads and 3D flow over non‐rotating MEXICO blades

This paper presents the experimental and numerical study on MEXICO wind turbine blades. Previous work by other researchers shows that large deviations exist in the loads comparison between numerical predictions and experimental data for the rotating MEXICO wind turbine. To reduce complexities and uncertainties, a non‐rotating experimental campaign has been carried out on MEXICO blades Delft University of Technology. In this new measurement, quasi‐2D aerodynamic characteristics of MEXICO blades on three spanwise sections are measured at different inflow velocities and angles of attack. Additionally, RANS simulations are performed with OpenFOAM‐2.1.1 to compare numerical results against measured data. The comparison and analysis of aerodynamic loads on the blade, where three different airfoil families and geometrical transition regions are used, show that for attached flow condition, RANS computation predicts excellent pressure distribution on the NACA airfoil section (r/R = 0.92) and good agreement is observed on the DU (r/R = 0.35) and RISØ (r/R = 0.60) airfoil sections. Unexpected aerodynamic characteristics are observed at the intermediate transition regions connecting the RISØ and DU airfoils, where sudden lift force drop is found at the radial position r/R = 0.55. Through numerical flow visualization, large‐scale vortical structures are observed on the suction side of the blade near the mid‐span. Moreover, counter‐rotating vortices are generated behind the blade at locations where unexpected loads occurs. Consequently, the RISØ airfoil could not give expected 2D aerodynamic characteristics because of upwash/downwash effects induced by these counter‐rotating vortices, which make 3D effects play an important role in numerical modeling when calculating the aerodynamic loads for MEXICO rotor. ©2016 The Authors Wind Energy Published by John Wiley & Sons Ltd     

Linear and non-linear analyses for semi-elliptical surface cracks in pipes under bending

In this paper, the J integral was calculated for semi-elliptical surface cracks in pipes under bending using three-dimensional finite element analysis. The computations were performed for elastic and elastic-plastic behaviours. For the elastic case, the numerical results allowed the extrapolation of shape functions for analytical determination of the J integral. The results are in a good agreement with those in the literature if the ratio between the radius and the thickness of the pipe (R/t) is from 1 to 10. The analysis was extended to values of the ratio R/t higher than 10. For the elastic-plastic, the numerical results are in good agreement with the analytical solution found in the literature for thick pipes (R/t ≥ 10). The effect of the ratio R/t becomes sensible when the ratio of the applied moment to the moment of reference (M/Mor) exceeds 0.9.