(582e) Direct Numerical Simulations of Miscible and Immiscible Product Changeover

Two-fluid flows are a prevalent phenomenon in both the natural world and various technological processes. In the environment, we see examples of this in the movement of lava during volcanic eruptions, the shifting of ice masses in glaciers, and the stratification of ocean waters (Govindarajan and Sahu, 2014; Sahu, 2021). In terms of industrial processes, this concept is significant in displacement flows, and liquid-liquid mixing, which can be accomplished using devices such as static mixers (Valdes et al., 2023) or stirred vessels (Liang et al., 2022). A specific industrial use is during product changeovers, which aim to clean pipelines efficiently while minimising wastewater utilisation. Moreover, an important application in the healthcare industry is the analysis of blood transport in the human body since artificial heart valves can cause flow conditions that lead to high stress levels and cause damage to blood cells (James et al., 2019). This has led to a wide range of research efforts involving experiments, theory, and simulations to better understand and utilise two-fluid flows.

This research examines the process of cleaning a horizontal cylindrical pipe of a diameter D that contains an initially static, viscous Newtonian fluid. The simulation setup is found in panel (a) of figure 1, where the length of the cylindrical pipe corresponds to 24D. The cleaning agent is a fluid less viscous than the displaced fluid, such that μ₂ > μ_1, and the study explores the dynamics under both laminar and turbulent flow conditions. The flow regimes are distinguished by their respective Reynolds numbers (Re = DUρ/μ₁), where U is the average velocity of the cleaning agent and ρ is its density. In this study, the cleaning and displaced fluids are neutrally-buoyant, such that ρ₂ = ρ₁. The two Reynolds numbers considered in this work are equal to 10³ , which is indicative of laminar flow, and 10⁴ signifying turbulent flow. The inflow velocity profile of the displacing fluid was adjusted for the different flow regimes. The range of viscosity ratios between the cleaning and resident fluids extends up to 10³ in this work, and the study considers flows in both the miscible and immiscible configurations.

In the miscible regime, a convective-diffusion equation is utilised for the concentration (C), where κ is the diffusivity. The diffusivity of the fluid is characterised by the Schmidt number, such that Sc = μ₁/ρκ = 975. In the immiscible regime, the surface tension between the two fluids is σ. The numerical framework used in this study is based on solving the continuity and the momentum (incompressible Navier-Stokes) equations (Shin et al., 2017). The simulations are carried out in a three-dimensional Cartesian domain x = (x, y, z), where x and y denote the two horizontal coordinates, and z denotes the vertical coordinate. A second-order Gear scheme was utilised for temporal discretisation, and the computational domain is divided into parallel subdomains, which are each uniformly discretised by a 32³ finite-difference mesh with a global grid resolution of 1536 × 64 × 64. The scalar variables, such as the concentration and pressure, are defined at the cell centres, whereas the velocity vector is defined at the cell faces. The massively parallel code implements an interface-capturing algorithm using a hybrid front-tracking level-set technique.

The results for the immiscible (miscible) laminar and turbulent cases where μ₂/μ₁ = 10³ are presented in panels (b) and (c) ((d) and (e)) of figure 1, respectively. The figure showcases the different types of patterns that tend to form due to the difference in viscosity between the two phases before reaching the pipe exit. In the laminar regime, this leads to the formation of sausage-like patterns driven by the shear at the interface. This pattern leads to a constriction at the interface which enhances the flow velocity at that region. Due to this enhancement, in the miscible configuration, the difference in velocity at the region between the flow centre and the diffuse interface leads to the formation of rollup Kelvin-Helmholtz instability which enhances the convective mixing. In the turbulent regime, the increased flow velocity of the cleaning agent leads to additional instabilities forming at the interface when the fluids are immiscible. As the velocity difference between the two phases is larger in the turbulent regime, the enhanced shear leads to roll-up patterns at the interface. In the miscible, turbulent case, a similar flow pattern was found with enhanced convective mixing near the pipe centre due to the formation of secondary instabilities. Because of the large viscosity ratios considered, reminiscent viscous fluid remains near the pipe walls and resists the imposing flow of the clean fluid. With the ultimate goal of cleaning the pipe, this study further considers the cleaning efficiency of the displacement flow as a function of the viscosity ratio in the laminar and turbulent regimes. A comprehensive overview of the different flow patterns and cleaning efficiencies in viscosity-stratified pipeline flows will be presented to further understand the rich dynamics.

Caption:

Figure 1: Panel (a) provides a representation of the pipeline configuration, where ρ₁ and ρ₂ are the fluid densities, and μ₁ and μ₂ are the fluid viscosities for the clean and viscous phases, respectively. For the immiscible case, σ is the surface tension between the two phases, whereas for the miscible case, κ denotes the diffusivity. Panels (b) and (c) showcase the flow pattern for the immiscible laminar and turbulent cases, respectively. Panels (d) and (e) are the flow patterns for the miscible laminar and turbulent cases, respectively, where the concentration profile due to mixing may be visualised by the colour bar.

Acknowledgements:

We acknowledge support through HPC/AI computing time at the Institut du Developpement et des Ressources en Informatique Scientifique (IDRIS) of the Centre National de la Recherche Scientifique (CNRS), coordinated by GENCI (Grand Equipement National de Calcul Intensif) grant 2023 A0142B06721. This work was supported by the Engineering and Physical Sciences Research Council, UK, through the MEMPHIS (EP/K003976/1) and PREMIERE (EP/T000414/1) programme grant. O.K.M. acknowledges funding from PETRONAS and the Royal Academy of Engineering for a Research Chair in Multiphase Fluid Dynamics. A.A. acknowledges the Kuwait Foundation for the Advancement of Sciences (KFAS) for their financial support. A.A. and L.K. acknowledge HPC facilities provided by the Imperial College London Research Computing Service.

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