Lumped models for transient thermal analysis of multilayered composite pipeline with active heating

In this study, improved lumped parameter models were proposed for transient thermal analysis of multilayered composite pipeline with active heating, which is essential for flow assurance design and operating strategies of deepwater subsea pipelines. Improved lumped models for transient heat conduction in multilayered composite pipelines were based on two-points Hermite approximations for integrals. The transient energy equation for the bulk temperature of the produced fluid was transformed into a set of ordinary differential equations in time by using a finite difference method. The coupled system of ordinary differential equations for average temperatures in the solids and bulk temperature of the fluid at each longitudinal discretization point along the pipeline was solved by using an ODE solver. With the proposed method, we analyzed the transient heat transfer in stainless steel-polypropylenestainless steel sandwich pipes (SP) with active electrical heating. Convergence behaviors of the average temperature of each layer and the bulk temperature of the produced fluid calculated by using the improved lumped models (H0,0/H1,1 and H1,1/H1,1 approximations) against the number of grid points along the pipelines were presented. Case studies were performed to investigate the effect of the linear rate of power input and the average velocity on the bulk temperature distribution of the produced fluid.Indisponível

Dynamic response of clamped axially moving beams: Integral transform solution

The generalized integral transform technique (GITT) is employed to obtain a hybrid analytical–numerical solution for dynamic response of clamped axially moving beams. The use of the GITT approach in the analysis of the transverse vibration equation leads to a coupled system of second order differential equations in the dimensionless temporal variable. The resulting transformed ODE system is then solved numerically with automatic global accuracy control by using the subroutine DIVPAG from IMSL Library. Excellent convergence behavior is shown by comparing the vibration displacement of different points along the beam length. Numerical results are presented for different values of axial translation velocity and flexural stiffness. A set of reference results for the transverse vibration displacement of axially moving beam is provided for future co-validation purposes.Indisponível

Dynamic Behavior of Axially Functionally Graded Pipes Conveying Fluid

Dynamic behavior of axially functionally graded (FG) pipes conveying fluid was investigated numerically by using the generalized integral transform technique (GITT). The transverse vibration equation was integral transformed into a coupled system of second-order differential equations in the temporal variable. The Mathematica’s built-in function, NDSolve, was employed to numerically solve the resulting transformed ODE system. Excellent convergence of the proposed eigenfunction expansions was demonstrated for calculating the transverse displacement at various points of axially FG pipes conveying fluid. The proposed approach was verified by comparing the obtained results with the available solutions reported in the literature. Moreover, parametric studies were performed to analyze the effects of Young’s modulus variation, material distribution, and flow velocity on the dynamic behavior of axially FG pipes conveying fluid

Dynamic behavior of pipes conveying gas–liquid two-phase flow

In this paper, the dynamic behavior of pipes conveying gas–liquid two-phase flow was analytically and numerically investigated on the basis of the generalized integral transform technique (GITT). The use of the GITT approach in the analysis of the transverse vibration equation lead to a coupled system of second order differential equations in the dimensionless temporal variable. The Mathematica's built-in function, NDSolve, was employed to numerically solve the resulting transformed ODE system. The characteristics of gas–liquid two-phase flow were represented by a slip-ratio factor model that was devised and used for similar problems. Good convergence behavior of the proposed eigenfunction expansions is demonstrated for calculating the transverse displacement at various points of pipes conveying air–water two-phase flow. Parametric studies were performed to analyze the effects of the volumetric gas fraction and the volumetric flow rate on the dynamic behavior of pipes conveying air–water two-phase flow. Besides, the normalized volumetric-flow-rate stability envelope for the dynamic system was obtained.Indisponível

Improved lumped models for transient combined convective and radiative cooling of multi-layer composite slabs

Improved lumped parameter models were developed for the transient heat conduction in multi-layer composite slabs subjected to combined convective and radiative cooling. The improved lumped models were obtained through two-point Hermite approximations for integrals. Transient combined convective and radiative cooling of three-layer composite slabs was analyzed to illustrate the applicability of the proposed lumped models, with respect to different values of the Biot numbers, the radiationconduction parameter, the dimensionless thermal contact resistances, the dimensionless thickness, and the dimensionless thermal conductivity. It was shown by comparison with numerical solution of the original distributed parameter model that the higher order lumped model (H1,1/H0,0 approximation) yielded significant improvement of average temperature prediction over the classical lumped model. In addition, the higher order (H1,1/H0,0) model was applied to analyze the transient heat conduction problem of steel-concrete-steel sandwich plates.Indisponível

Exact solution of bending problem of clamped orthotropic rectangular thin plates

The generalized integral transform technique (GITT) is employed to obtain an exact solution for the bending problem of fully clamped orthotropic rectangular thin plates. The use of the GITT approach in the analysis of the transverse deflection equation leads to a coupled system of fourth order differential equations (ODEs) in the dimensionless longitudinal spatial variable. The resulting transformed ODE system is then numerically solved by making use of the subroutine DBVPFD from IMSL Library. Numerical results with automatic global accuracy control are obtained for different values of aspect ratio. Critical comparisons with previously reported numerical results are performed with excellent agreement. A set of reference results for clamped orthotropic rectangular plates is also provided for future covalidation purposes, which are verified by those obtained from the general-purpose finite element software package ABAQUS.Indisponível

Integral transform solutions of dynamic response of a clamped–clamped pipe conveying fluid

Analysis of dynamic response of pipe conveying fluid is an important aspect in nuclear power plant design. In the present paper, dynamic response of a clamped–clamped pipe conveying fluid was solved by the generalized integral transform technique (GITT). The governing partial differential equation was transformed into a set of second-order ordinary differential equations which is then numerically solved by making use of the subroutine DIVPAG from IMSL Library. A thorough convergence analysis was performed to yield sets of reference results of the transverse deflection at different time and spanwise position. We found good agreement between the computed natural frequencies at mode 1–3 and those obtained by previous theoretical study. Besides, modal separation analysis was carried out and the influence of mass ratio on deflection and natural frequencies was qualitatively and quantitatively assessed.Indisponível

Prediction of Vortex-Induced Vibration of Long Flexible Cylinders Modeled by a Coupled Nonlinear Oscillator: Integral Transform Solution

The Generalized Integral Transform Technique (GITT) was applied to predict dynamic response of Vortex-Induced Vibration (VIV) of a long flexible cylinder. A nonlinear wake oscillator model was used to represent the cross-flow force acting on the cylinder, leading to a coupled system of second-order Partial Differential Equations (PDEs) in temporal variable. The GITT approach was used to transform the system of PDEs to a system of Ordinary Differential Equations (ODEs), which was numerically solved by using the Adams-Moulton and Gear method (DIVPAG) developed by the International Mathematics and Statistics Library (IMSL). Numerical results were presented for comparison to those given by the finite difference method and experimental results, allowing a critical evaluation of the technique performance. The influence of variation of mean axial tension induced by elongation of flexible cylinder was evaluated, which was shown to be not negligible in numerical simulation of VIV of a long flexible cylinder.Indisponível

Improved Lumped Models for Transient Combined Convective and Radiative Cooling of Multilayer Spherical Media

In this work, we studied the transient combined convection and radiation of multilayer spherical media with volumetric heat generation, extending the previous work on the particular case of a spherical body subjected to radiative cooling. The proposed lumped models were obtained through two-point Hermite approximations for the average temperature and heat flux in each layer. For the average temperature, the plain trapezoidal rule (H0,0 approximation) was employed in all layers, except for the innermost layer, where the second-order two-side corrected trapezoidal rule (H2,1 approximation) was utilized. For the heat flux, the plain trapezoidal rule (H0,0 approximation) was employed for all the layers. The transient heat conduction in a TRISO-coated fuel particle being composed of five layers (namely, fuel kernel, buffer of porous carbon, inner pyrocarbon, silicon carbide, and outer pyrocarbon) was analyzed using the proposed lumped models, the results of which were verified by comparison with the finite difference solution of the original distributed parameter model. Parametric studies were conducted to examine the effects of the dimensionless heat generation rate, the radiation-conduction parameter, and the Biot number on the temporal variations of the average temperatures