Constitutive model and failure locus of a polypropylene grade used in offshore intake pipes

BorECO^®™ BA212E is a polypropylene block co-polymer which has become a common material in the manufacturing of large diameter non-pressurized gravity offshore intake pipelines. These lines are used for transportation of sea water for cooling of petrochemical process plants. The pipe sections are joined by butt heat fusion welding to create the pipeline. Recently a few premature failures of such pipelines have been reported in the field. Hence, there is a need to characterize the constitutive behavior of the pipe and weld material in order to properly design these pipes. The aim of this work is to determine the material constitutive behaviors of the pipe material and the welded joint material. Uniaxial tensile tests of both the pipe and weld joint material are conducted at various strain rates. Both the pipe and weld material show a rather high strain rate dependency, with the weld material having about half the yield strength than that of the pipe material. An analytical constitutive material model is developed for both the pipe and weld material, incorporating the effect of strain rate. The failure locus, expressed in terms of the equivalent plastic strain at failure vs. the stress triaxiality, for both materials is also determined as part of the constitutive model using notched dumbbell specimens. The constitutive model and failure loci for the pipe and weld material are implemented in a finite element model (FEM) and are validated by conducting a series of independent four-point bend experiments on both material types. The validation is carried out by comparing the FEM results of the four-point bend model with the experimental results, which show a rather good agreement.     

A new perspective on k-triangulations

We connect k-triangulations of a convex n-gon to the theory of Schubert polynomials. We use this connection to prove that the simplicial complex with k-triangulations as facets is a vertex-decomposable triangulated sphere, and we give a new proof of the determinantal formula for the number of k-triangulations.     

Turbulent stresses and particle break-up criteria in particle-laden pipe flows

Three-dimensional particle tracking velocimetry (3D-PTV) is applied to particle-laden pipe flows at Reynolds number 10,300, based on the bulk velocity and the pipe diameter. The effects of flow direction (upward or downward) and mean concentration (in the range 0.5 × 10⁻⁵–3.2 × 10⁻⁵) on the production of turbulence are assessed for inertial particles with a Stokes number equal to 2.3, based on the particle relaxation time and viscous scales. The turbulence production and the Kolmogorov constant, both measured for particle laden flows in upflow and downflow, allowed for the derivation of a break-up criterion as a function of the radial coordinate. This criterion predicts the maximum possible particle size before break-up may occur. It is shown that the maximum particle size is bigger at the pipe centerline than in the near-wall zone by more than a factor of 5. Flow direction affects the particle concentration profile, with wall peaking in downflow and core peaking in upflow. This affects both the residence time and the maximum particle size, the latter by 7%.     

Acoustic measurements of the infinitesimal phase response curve from a sounding organ pipe

The infinitesimal phase response curve (iPRC) of an organ pipe was measured using two types of external forcing, namely, sinusoidal and pulse forcing. Although the measured iPRCs exhibited different shapes because of the difficulty in realizing ideal pulses in acoustic experiments, the spectral structures agreed between both methods. Both measurements indicated that an external sound, which matched the pipe's second resonance, could most effectively induce frequency locking. Acoustically, this may be considered as a consequence of the pipe's open end. Our study is of significant importance in understanding the characteristics of frequency locking among organ pipes.     

Directional wave separation in tubular acoustic systems – The development and evaluation of two industrially applicable techniques

An acoustic device is used to evaluate internal features and defects within tubes by determination of the acoustic impulse response. This paper concerns methods of separating the total pressure wave measured in the device into its forward and backward travelling components, which facilitates computation of the acoustic impulse response. The device comprises a tube that has a speaker at one end and is axially instrumented with microphones. Unlike similar works, the methods presented in this paper were designed to be applied in an industrial context, they allow simple calibration and implementation using readily transportable equipment. Two wave separation algorithms are presented; the first is a known method that has been improved to provide simplified calibration and the second is a computationally inexpensive technique that has been adapted to improve its operational bandwidth. The techniques are critically evaluated using a custom built test rig, designed to simulate realistic tube features and defects such as constrictions, holes and corrosion. It is demonstrated that, although inter-microphone attenuation is not accounted for in the second algorithm, both algorithms function well and give similar results. It is concluded that the added sophistication of the first method means that it is less affected by low frequency interference and is capable of yielding more accurate results. However, in practical use as an evaluation tool, the benefits of including inter-microphone attenuation are outweighed by the additional calibration and computational requirements. Finally the output of the wave separation techniques is validated by showing agreement between experimental impulse response measurements and those obtained from a theoretically derived acoustic tube simulator.     

Nonlinear dynamics of cantilevered pipes conveying fluid: Towards a further understanding of the effect of loose constraints

The nonlinear dynamics of a fluid-conveying cantilevered pipe with loose constraints placed somewhere along its length is investigated. The main objective of this study is to determine the effects of several geometrical and physical parameters of the loose constraints on the characteristics and behavior of pipes conveying fluid. Based on the full nonlinear equation of motion, the dynamical behavior of the pipe system is investigated. Phase portraits and bifurcation diagrams are constructed for a selected set of system parameters. Typical results are firstly compared to numerical ones reported previously and excellent agreement is obtained. Then, the threshold flow velocities for several key bifurcations including pitchfork, period doubling, chaos, and sticking behaviors are predicted, showing that in many cases, the gap size, stiffness, and asymmetry of the loose constraints have remarkable effects on the nonlinear responses of the cantilevered pipe conveying fluid. For a pipe system with small/large constraint gap sizes, small constraint stiffness, or large constraint offset, some of the complex dynamical behaviors including chaos and period-doubling bifurcations would disappear, at least in the flow velocity range of interest.     

Gröbner bases for solving ΔQ-equations in water distribution networks

The analysis of water distribution network is of great interest to hydraulic engineers. Although the water distribution network has been extensively studied for the last decades, there are still many unsolved problems awaiting clarification. In this paper, an algorithm is presented that describes a computationally efficient technique for water distribution networks based on Gröbner basis method. Gröbner basis algorithm provides the exact algorithmic solutions for solving the system of equations. However, Gröbner algorithm works only for polynomials and moreover for a large scale network, it takes a long CPU time. Hence, we present two other algorithms that work for non-polynomials and large scale problems. Three examples are presented to show the effectiveness of Gröbner basis method compared with Hardy Cross method, linear theory and Gradient method.     

A virtual pipe rig for testing acoustic leak detection correlators: Proof of concept

Acoustic correlators have been used for many years to locate and detect leaks in buried water distribution pipes. Currently, the only way to compare different correlators directly is in the field. This can be problematic as it may be difficult to present exactly the same conditions to each correlator. In recent years, the way in which leak noise propagates in buried water pipes has been determined, and this has enabled the development of a virtual pipe whose behaviour can be simulated in the computer. By coupling the filtering properties of the pipe with electrodynamic shakers, a proof-of-concept virtual pipe test-rig has been developed that will allow different correlators to be compared directly in laboratory conditions. Different situations, such as pipe material and size, and measurement positions, as well as leak strength can be simulated. The theoretical basis of the test-rig and details of the proof-of-concept system are discussed in this paper. It is shown that careful consideration of the dynamics of the shakers is vital if the system is to faithfully model situations that are found in the field.