The accuracy, robustness, dissipation characteristics and efficiency of several structured and unstructured grid methods are investigated with reference to the low Mach double vortex pairing flow problem. The aim of the study is to shed light into the numerical advantages and disadvantages of different numerical discretizations, principally designed for shock-capturing, in low Mach vortical flows. The methods include structured and unstructured finite volume and Lagrange-Remap methods, with accuracy ranging from 2nd to 9th-order, with and without applying low-Mach corrections. Comparison of the schemes is presented for the vortex evolution, momentum thickness, as well as for their numerical dissipation versus the viscous and total dissipation. The study shows that the momentum thickness and large scale features of a basic vortical structure are well resolved even at the lowest grid resolution of 32×32 provided that the numerical schemes are of a high-order of accuracy or the numerical framework is sufficiently non-dissipative. The implementation of the finite volume methods in unstructured triangular meshes provides the best results even without low Mach number corrections provided that a higher-order advective discretization for the advective fluxes is employed. The compressible Lagrange-Remap framework is computationally the fastest one, although the numerical error for the momentum thickness does not reduce as fast as for other numerical schemes and computational frameworks, e.g., when higher-order schemes are utilized. It is also shown that the low-Mach number correction has a lesser effect on the results as the order of the spatial accuracy increases
This paper introduces a unified concept and algorithm for the fractional-step (FS), artificial compressibility (AC) and pressure-projection (PP) methods for solving the incompressible Navier-Stokes equations. The proposed FSAC-PP approach falls into the group of pseudo-time splitting high-resolution methods incorporating the characteristics-based (CB) Godunov-type treatment of convective terms with PP methods. Due to the fact that the CB Godunov-type methods are applicable directly to the hyperbolic AC formulation and not to the elliptical FS-PP (split) methods, thus the straightforward coupling of CB Godunov-type schemes with PP methods is not possible. Therefore, the proposed FSAC-PP approach unifies the fully-explicit AC and semi-implicit FS-PP methods of Chorin including a PP step in the dual-time stepping procedure to a) overcome the numerical stiffness of the classical AC approach at (very) low and moderate Reynolds numbers, b) incorporate the accuracy and convergence properties of CB Godunov-type schemes with PP methods, and c) further improve the stability and efficiency of the AC method for steady and unsteady flow problems. The FSAC-PPmethod has also been coupled with a non-linear, full-multigrid and fullapproximation storage (FMG-FAS) technique to further increase the efficiency of the solution. For validating the proposed FSAC-PP method, computational examples are presented for benchmark problems. The overall results show that the unified FSAC-PP approach is an efficient algorithm for solving incompressible flow problems.
A multiphase approach is used to study macrosegregation phenomena that occur during solidification of steel ingot castings. The goal is to enhance the understanding of different mechanisms of macrosegregation formation. 4 different cases are presented consecutively with increasing complexity of the model assumptions and increasing dimensions: (1) feeding-induced macrosegregations in 1-dimentional unidirectional solidification situation, (2) macrosegregations caused by thermosolutal buoyancy driven flow in a 2-dimensional axially symmetric benchmark ingot, (3) macrosegregations caused by grain sedimentation in the same 2-dimensional ingot, and (4) macrosegregations which form during mixed equiaxed-columnar solidification in a full 3-dimensional benchmark ingot.
This paper focuses on the analysis of the possibility of domino effect in underground parallel pipelines relying on historical accident data and pipeline crater models. An underground pipeline can be considered as safe following an accident with an adjacent gas or liquefied pipeline when it remains outside the ground crater generated. In order to prevent the domino effect in these cases, the design of parallel pipelines has to consider adequate pipeline separations based on the crater width, which is one of the widely used methods in engineering applications. The objective of this work is the analysis of underground petroleum product pipelines ruptures with the formation of a ground crater as well as the evaluation of possible domino effects in these cases. A detailed literature survey has been carried out to review existing crater models along with a historical analysis of past accidents. A FORTRAN code has been implemented to assess the performance of the Gasunie, the Batelle and the Advantica crater models. In addition to this, a novel Accident-Based crater model has been presented, which allows the prediction of the crater width as a function of the relevant design pipeline parameters as well as the soil density. Modifications have also been made to the Batelle and Accident-Based models in order to overcome the underestimation of the crater width. The calculated crater widths have been compared with real accident data and the performance evaluation showed that the proposed Accident-Based model has a better performance compared to other models studied in this work. The analysis of forty-eight past accidents indicated a major potential of underground parallel pipelines domino effect which is proven by two real cases taken from the literature. Relying on the investigated accidents, the crater width was smaller than or equal to 20 meters in most cases indicating that the definition of underground pipeline separations at around 10 meters would be sufficient to ensure a small probability of the domino effect.
A mixed columnar-equiaxed solidification model is used to predict the macrosegregation in high grade steel ingots. In this model, three phases are considered: the melt; the columnar phase, which is assumed to be stationary; and the equiaxed phase, which is free to move. With this approach, the model is able to simulate the evolution of the primary solid phase distributions including the columnar-to-equiaxed transition, the melt convection and the grain sedimentation, and their influence on the macrosegregation. Thermodynamic information of a ternary alloy (Fe-C-Cr) is simplified by the piecewise linearization of the phase diagram around the suitable compositions in the ferritic and austenitic regions. As a result, macrosegregation of carbon and chromium has been analyzed. As the first step, the validation of the numerical model was performed on a benchmark ingot of a laboratory scale. Computed macrosegregation and primary structure were compared with measurements and good agreement was obtained.
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