Thermoelastic Coupling Response of an Unbounded Solid with a Cylindrical Cavity Due to a Moving Heat Source

The current article introduces the thermoelastic coupled response of an unbounded solid with a cylindrical hole under a traveling heat source and harmonically altering heat. A refined dual-phase-lag thermoelasticity theory is used for this purpose. A generalized thermoelastic coupled solution is developed by using Laplace’s transforms technique. Field quantities are graphically displayed and discussed to illustrate the effects of heat source, phase-lag parameters, and the angular frequency of thermal vibration on the field quantities. Some comparisons are made with and without the inclusion of a moving heat source. The outcomes described here using the refined dual-phase-lag thermoelasticity theory are the most accurate and are provided as benchmarks for other researchers.

Application of Population-Based Techniques to Identification of Diffusive and Convective Parameters in Timber Drying

Timber drying consists of reducing the moisture content up to a level required by the intended application of the wood product. A proper drying operation is essential to reduce time and energy, as well as to prevent defects. Numerical simulation of this class of problems constitutes an important tool available to the process engineer to define the best drying schedule. However, a successful prediction requires knowledge of the wood properties and additional process parameters. This work is inserted within this framework and aims at discussing strategies do determine material and process parameters using inverse problem techniques. The timber drying process accounts for the fully coupled solution of the heat and mass (moisture) transfer problem, whereas the inverse problem is solved within the time domain based on population-based optimization techniques.

Inexact Methods for Black-Oil Sequential Fully Implicit SFI Scheme

The sequential fully implicit (SFI) scheme was introduced (Jenny et al. 2006) for solving coupled flow and transport problems. Each time step for SFI consists of an outer loop, in which there are inner Newton loops to implicitly and sequentially solve the pressure and transport sub-problems. In standard SFI, the sub-problems are usually fully solved at each outer iteration. This can result in wasted computations that contribute little towards the coupled solution. The issue is known as ‘over-solving’. Our objective is to minimize the cost while maintain or improve the convergence of SFI by preventing ‘over-solving’. We first developed a framework based on the nonlinear acceleration techniques (Jiang and Tchelepi 2019) to ensure robust outer-loop convergence. We then developed inexact-type methods that prevent ‘over-solving’ and minimize the cost of inner solvers for SFI. The motivation is similar to the inexact Newton method, where the inner (linear) iterations are controlled in a way that the outer (Newton) convergence is not degraded, but the overall computational effort is greatly reduced. We proposed an adaptive strategy that provides relative tolerances based on the convergence rates of the coupled problem. The developed inexact SFI method was tested using numerous simulation studies. We compared different strategies such as fixed relaxations on absolute and relative tolerances for the inner solvers. The test cases included synthetic as well as real-field models with complex flow physics and high heterogeneity. The results show that the basic SFI method is quite inefficient. When the coupling is strong, we observed that the outer convergence is mainly restricted by the initial residuals of the sub-problems. It was observed that the feedback from one inner solver can cause the residual of the other to rebound to a much higher level. Away from a coupled solution, additional accuracy achieved in inner solvers is wasted, contributing to little or no reduction of the overall residual. By comparison, the inexact SFI method adaptively provided the relative tolerances adequate for the sub-problems. We show across a wide range of flow conditions that the inexact SFI can effectively resolve the ‘over-solving’ issue, and thus greatly improve the overall performance. The novel information of this paper includes: 1) we found that for SFI, there is no need for one sub-problem to strive for perfection (‘over-solving’), while the coupled residual remains high because of the other sub-problem; 2) a novel inexact SFI method was developed to prevent ‘over-solving’ and minimize the cost of inner solvers; 3) an adaptive strategy was proposed for relative tolerances based on the convergence rates of the coupled problem; and 4) a novel SFI framework was developed based on the nonlinear acceleration techniques to ensure robust outer-loop convergence.

Coupling-Strength Criteria for Sequential Implicit Formulations

Sequential Fully Implicit (SFI) schemes have been proposed as an alternative to the Fully Implicit Method (FIM). A significant advantage of SFI is that one can employ scalable strategies to the flow and transport problems. However, the primary disadvantage of using SFI compared with FIM is the fact that the splitting errors induced by the decoupling operator, which separates the pressure from the saturation(s), can lead to serious convergence difficulties of the overall nonlinear problem. Thus, it is important to quantify the coupling strength in an adaptive manner in both space and time. We present criteria that localize the computational cells where the pressure and saturation solutions are tightly coupled. The approach is using terms in the FIM Jacobian matrix, we quantify the sensitivity of the mass and volume-balance equations to changes in the pressure and the saturations. We identify three criteria that provide a measure of the coupling strength across the equations and variables. The standard CFL stability criteria, which are based entirely on the saturation equations, are a subset of the new criteria. Here, the pressure equation is solved using Algebraic MultiGrid (AMG), or a multiscale solver, such as the Multiscale Restricted-Smooth Basis (MsRSB) approach. The transport equations are then solved using a fixed total-velocity. These ‘coupling strength’ criteria are used to identify the cells where the pressure-saturation coupling is strong. The applicability of the derived coupling-strength criteria is tested using several test cases. The first test is using a gravitational immiscible dead-oil lock-exchange under a unit mobility ratio and large differences in density. For this case, the SFI algorithm fails to converge to the fully coupled solution due to the large splitting errors. Introducing a fully coupled solution stage on the local subdomains as an additional correction step restores nonlinear convergence. Detailed analysis of the ‘coupling strength’ criteria indicates that the criteria related to the sensitivity of the mass balance to changes in the pressure and the sensitivity of the volume balance to changes in the saturations are the most important ones to satisfy. Other test cases include an alternate gas-water-gas injection in a top layer of the SPE 10 test case and an injection-production scenario in a three-dimensional reservoir with layered lognormally distributed permeability. We propose novel criteria to estimate the strength of coupling between pressure and saturation. These CFL-like numbers are used to identify the cells that require fully implicit treatment in the nonlinear solution strategy. These criteria can also be used to improve the nonlinear convergence rates of Adaptive Implicit Methods (AIM).

A One-Way Coupled Hydrodynamic Advection-Diffusion Model to Simulate Congested Large Wood Transport

An advection-diffusion model is proposed to simulate large wood transport during high flows. The mathematical model is derived from the wood mass balance, taking into consideration both the wood mass concentration and the log orientation, which affects log transport and, most importantly, wood accumulation. Focusing on wood mass transport, the advection-diffusion equation is implemented in a hydrodynamic model to provide a one-way coupled solution of the flow and of the floating wood mass. The model is tested on a large series of flume experiments, involving at least 30 logs and different control parameters (flow Froude number, log length, diameter, release point). The validation through the experimental data shows that the proposed model can predict the correct displacement of the most probable position of the logs and to simulate with a sufficient accuracy the planar diffusion of the wooden mass. Transversal wood distribution is more accurate than the streamwise one, indicating that a higher control on the longitudinal diffusion needs to be implemented.

Numerical investigations on solute transport and freckle formation during directional solidification of nickle-based superalloy ingot

In order to investigate the solute distribution and freckles formation during directional solidification of superalloy ingots, a mathematical model with coupled solution of flow field, solute and temperature distribution was developed. Meanwhile, the reliability of this model was verified by the experimental and simulation results in relevant literatures. The three-dimensional directional solidification process of Ni-5.8wt%Al-15.2wt%Ta superalloy ingot was simulated, and then the dynamic growth of solute enrichment channels was demonstrated inside the ingot. Freckles formation under different cooling rates was studied, and the local segregation degree inside the ingot was obtained innovatively after solidification. The results show that the number of freckles formed at the top gradually decreases, and so do the degree of solute enrichment at these freckles with the increase of cooling rate. Moreover, the relative and volume-averaged segregation ratio is defined to describe the segregation degree inside the ingot. The span of relative segregation ratio for positive segregation is wider than that for negative segregation, but it accounts for less of total volume. As the cooling rate increases from 0.1 K/s to 1.0 K/s, the proportion of weak segregation (-20%~20%) increases significantly from 26% to 41%, so that the segregation degree is weakened in general. By analyzing the freckles formation and segregation degree inside the ingot, the numerical simulation results can provide a theoretical basis for optimizing the actual production process to suppress the freckle defects.

Coupled tribo-dynamic modelling of linear guideways for high precision machining application

Linear guideways play a crucial role in determining precision of machine tools. Understanding their dynamic response is essential for objectively controlling their behavior and performance in operation. Due to highly loaded lubricated contacts, mixed-elastohydrodynamic regime is dominant. The mixed-elastohydrodynamic film maintains the coupling between horizontal degree of freedom (feed velocity) and vertical degree of freedom (loading direction). This paper presents a novel tribo-dynamic solution for linear guideways, taking in to account the lubricant effects and coupling between horizontal and vertical degrees of freedom. An analytical tribology model is used implicitly within the dynamic model. For in-depth tribological quantities including pressure and film thickness distribution, an explicit full numerical solution for mixed-elastohydrodynamic is utilized. Results show that the coupled solution of vertical and horizontal degrees of freedom taking in to account lubricated contacts is essential. It is shown that at moderate and light loads, the effect of this coupling and presence of lubricant is more pronounced.