@misc{Le2024, author = {Le, Thi Thai}, title = {Effect of viscous forces on the interface stability of a tangential-velocity discontinuity in compressible fluids}, journal = {Journal}, year = {2024}, abstract = {Compressible flows are prevalent in natural and technological processes, particularly in the energy transition to renewable energy systems. Consequently, extensive research has focused on understanding the stability of tangential--velocity discontinuity in compressible media. Despite recent advancements that address industrial challenges more realistically, many studies have ignored viscous stress tensors' impact, leading to inaccuracies in predicting interface stability. This omission becomes critical, especially in high Reynolds or low Mach number flows, where viscous forces dissipate kinetic energy across interfaces, affect total energy dissipation, and dampen flow instabilities. Our work is thus motivated to analyze the viscosity force effect by including the viscous stress tensor terms in the motion equations. Our results show that by considering the effect of viscous forces, the tangential-velocity discontinuity interface is constantly destabilized for the entire range of the Mach number.}, language = {en} } @article{PedersenLeKochetal.2024, author = {Pedersen, Jaap and Le, Thi Thai and Koch, Thorsten and Zittel, Janina}, title = {Optimal discrete pipe sizing for tree-shaped CO2 networks}, volume = {46}, journal = {OR Spectrum}, doi = {10.1007/s00291-024-00773-z}, pages = {1163 -- 1187}, year = {2024}, abstract = {For industries like the cement industry, switching to a carbon-neutral production process is impossible. They must rely on carbon capture, utilization and storage (CCUS) technologies to reduce their production processes' inevitable carbon dioxide (CO2) emissions. For transporting continuously large amounts of CO2, utilizing a pipeline network is the most effective solution; however, building such a network is expensive. Therefore minimizing the cost of the pipelines to be built is extremely important to make the operation financially feasible. In this context, we investigate the problem of finding optimal pipeline diameters from a discrete set of diameters for a tree-shaped network transporting captured CO2 from multiple sources to a single sink. The general problem of optimizing arc capacities in potential-based fluid networks is already a challenging mixed-integer nonlinear optimization problem. The problem becomes even more complex when adding the highly sensitive nonlinear behavior of CO2 regarding temperature and pressure changes. We propose an iterative algorithm splitting the problem into two parts: a) the pipe-sizing problem under a fixed supply scenario and temperature distribution and b) the thermophysical modeling, including mixing effects, the Joule-Thomson effect, and heat exchange with the surrounding environment. We demonstrate the effectiveness of our approach by applying our algorithm to a real-world network planning problem for a CO2 network in Western Germany. Further, we show the robustness of the algorithm by solving a large artificially created set of network instances.}, language = {en} } @article{LeFukumoto2022, author = {Le, Thi Thai and Fukumoto, Yasuhide}, title = {Effect of depth discontinuity on interfacial stability of tangential-velocity discontinuity in shallow-water flow}, volume = {436}, journal = {Physics Letters A}, publisher = {ELSEVIER}, doi = {10.1016/j.physleta.2022.128073}, pages = {128073}, year = {2022}, abstract = {It is well known as the Kelvin-Helmholtz instability (KHI) that an interface of tangential velocity discontinuity is necessarily unstable, regardless of the velocity difference's strength. However, the KHI is suppressed for shallow water flows if the Froude number, defined by the ratio of the velocity difference to the gravity wave's speed, is sufficiently large. In this investigation, we examine the effect of the depth difference of two fluid layers on the KHI. The depth difference enhances instability. Given the Froude number in the instability range, the growth rate sensitively depends on the depth ratio and increases monotonically with the depth ratio difference from unity. The critical value of the Froude number for stabilization varies with the depth ratio and attains the minimum value √8 for equal depth. This behavior is verified by asymptotic analysis.}, language = {en} } @article{LeKoch2021, author = {Le, Thi Thai and Koch, Thorsten}, title = {Interface stability of compressible fluids in porous media}, volume = {33}, journal = {Physics of Fluids}, number = {8}, publisher = {AIP Publishing}, doi = {10.1063/5.0059336}, pages = {084102}, year = {2021}, abstract = {The stability of flows in porous media plays a vital role in transiting energy supply from natural gas to hydrogen, especially for estimating the usability of existing underground gas storage infrastructures. Thus, this research aims to analyze the interface stability of the tangential-velocity discontinuity between two compressible gases by using Darcy's model to include the porosity effect. The results shown in this research will be a basis for considering whether underground gas storages in porous material can be used to store hydrogen. We show the relation between the Mach number M, the viscosity \mu, and the porosity \epsilon on the stability of the interface. This interface stability affects gases' withdrawal and injection processes, thus will help us to determine the velocity which with gas can be extracted and injected into the storage effectively. By imposing solid walls along the flow direction, the critical values of these parameters regarding the stability of the interface are smaller than when considering no walls. The consideration of bounded flows approaches the problem more realistically. In particular, this analysis plays a vital role when considering two-dimensional gas flows in storages and pipes.}, language = {en} } @article{JinLeFukumoto2019, author = {Jin, Liangbing and Le, Thi Thai and Fukumoto, Yasuhide}, title = {Frictional effect on stability of discontinuity interface in tangential velocity of a shallow-water flow}, volume = {383}, journal = {Physics Letters A}, number = {26}, doi = {10.1016/j.physleta.2019.125839}, pages = {125839}, year = {2019}, abstract = {We examine a frictional effect on the linear stability of an interface of discontinuity in tangential velocity. The fluid is moving with uniform velocity U in a region but is at rest in the other, and the bottom surface is assumed to exert drag force, quadratic in velocity, on the thin fluid layer. In the absence of the drag, the instability of the Kelvin-Helmholtz type is suppressed for U>√8 c, with c being the propagating speed of the gravity wave. We find by asymptotic analyses for both small and large values of the drag strength that the drag, regardless of its strength, makes the flow unstable for the whole range of the Froude number U/c.}, language = {en} } @article{Le2019, author = {Le, Thi Thai}, title = {Kelvin-Helmholtz instability in a shallow-water flow with a finite width}, volume = {60}, journal = {Journal of Mathematical Physics}, number = {1}, publisher = {AIP Publishing}, doi = {10.1063/1.5126321}, pages = {123101}, year = {2019}, abstract = {We examine an effect of side walls on the linear stability of an interface of tangential-velocity discontinuity in shallow-water flow. The flow is pure horizontal in the plane xy, and the fluid is bounded in a finite width 2d in the y- direction. In region 0 < y < d, the fluid is moving with uniform velocity U but is at rest for -d < y < 0. Without side walls, the flow is unstable for a velocity difference U<√8c U < √8 c, with c being the velocity of gravity waves. In this work, we show that if the velocity difference U is smaller than 2c, the interface is always destabilized, also known as the flow is unstable. The unstable region of an infinite width model is shrunken by the effects of side walls in the case of narrow width, while there is no range for the Froude number for stabilization in the case of large width. These results play an important role in predicting the wave propagations and have a wide application in the fields of industry. As a result of the interaction of waves and the mean flow boundary, the flow is unstable, which is caused by a decrease in the kinetic energy of disturbance.}, language = {en} } @article{Le2021, author = {Le, Thi Thai}, title = {Effect of water depth on Kelvin - Helmholtz instability in a shallow-water flow}, volume = {62}, journal = {Journal of Mathematical Physics}, number = {10}, publisher = {AIP Publishing}, doi = {10.1063/1.5145060}, pages = {103101}, year = {2021}, abstract = {It is well known that the interface between two regions of an incompressible ideal fluid flow moving in a relative motion is necessarily destabilized, regardless of the velocity difference's strength. This phenomenon is the so-called Kelvin-Helmholtz instability (KHI). However, a large number of works demonstrated a surprising result that the instability is suppressed for shallow water flows; the interface is stabilized if the Froude number, defined by the velocity difference's ratio to the gravity wave's speed, is sufficiently large. In a limited way, these authors have been used the shallow-water equations without the higher-order effect of the dispersive terms. Thus, this investigation aims to examine these higher-order dispersive effects to analyze the interface stability problem of tangential-velocity discontinuity in shallow-water flows. In particular, we use the Green-Naghdi equations to introduce the dispersive terms related to the depth and the depth-averaged horizontal velocities of the fluid. We show that the interface stability depends on the Froude number (i.e., the velocity difference's strength) and the water depth. A critical value of the Froude number to stabilize the interface is smaller than the case of no dispersive terms, and the flow in a deeper region is more stable than in a shallower one. We also consider the distribution of kinetic and potential energy to clarify a feature characteristic of a large class of instabilities in shallow water flow. The instability of flows is caused by the decrease in the kinetic energy during the perturbation of waves. This phenomenon is known as negative energy modes and plays a vital role in applying the model to industrial equipment. A conclusion is that the equipartition of energies occurs if and only if the velocity difference is zero and the water depth is shallow enough to ignore the dispersive terms.}, language = {en} } @article{LeKoch2023, author = {Le, Thi Thai and Koch, Thorsten}, title = {Effect of inertia force on the interface stability of a tangential-velocity discontinuity in porous media}, volume = {169}, journal = {International Journal of Multiphase Flow}, doi = {10.1016/j.ijmultiphaseflow.2023.104612}, year = {2023}, abstract = {The present study investigates the stability of a tangential-velocity discontinuity in porous media during the withdrawing and injecting processes of natural gases from and into an underground gas storage. The focus is placed on analyzing the impact of inertia forces on the interface stability using the Forchheimer equations. Other publications have relied primarily on Darcy's law to describe flow stability in porous media. However, Darcy's law only adequately describes flows in which viscous forces dominate over inertia forces. As the flow rate increases, the significance of inertia forces becomes more pronounced, and Darcy's law becomes insufficient for considering such flows. Our findings indicate that even a slight consideration of the inertia effect leads to permanent destabilization of the discontinuity interface, regardless of the fluid viscosity or the Mach number. In contrast, when the inertia effect is neglected, the interface is stabilized across the entire Mach number range if the fluid viscosity is strong enough.}, language = {en} } @article{LePetkovic2025, author = {Le, Thi Thai and Petkovic, Milena}, title = {Predicting Fluid Interface Instability in Energy Systems for Sustainable Energy Transition}, journal = {Operations Research Proceedings 2023. OR 2023.}, publisher = {Springer}, doi = {10.1007/978-3-031-58405-3_45}, pages = {349 -- 356}, year = {2025}, abstract = {Due to the coexistence of different gases in underground storage, this work explores the interface stability's impact on energy storage, specifically during the injection and withdrawal of gases such as hydrogen and natural gas. A new approach of combing simulation and time series analysis is used to accurately predict instability modes in energy systems. Our simulation is based on the 2D Euler equations, solved using a second-order finite volume method with a staggered grid. The solution is validated by comparing them to experimental data and analytical solutions, accurately predicting the instability's behavior. We use time series analysis and state-of-the-art regime-switching methods to identify critical features of the interface dynamics, providing crucial insights into system optimization and design.}, language = {en} } @article{LeTranPhung2016, author = {Le, Thi Thai and Tran, Van Cuc and Phung, Dang Hieu}, title = {Numerical simulation of tidal flow in Danang Bay Based on non-hydrostatic shallow water equations}, volume = {8}, journal = {Pacific Journal of Mathematics for Industry}, number = {1}, doi = {10.1186/s40736-015-0020-6}, year = {2016}, abstract = {This paper presents a numerical simulation of the tidal flow in Danang Bay (Vietnam) based on the non-hydrostatic shallow water equations. First, to test the simulation capability of the non-hydrostatic model, we have made a test simulation comparing it with the experiment by Beji and Battjes 1993. Simulation results for this case are compared with both the experimental data and calculations obtained from the traditional hydrostatic model. It is shown that the non-hydrostatic model is better than the hydrostatic model when the seabed topography variation is complex. The usefulness of the non-hydrostatic model is father shown by successfully simulating the tidal flow of Danang Bay.}, language = {en} } @article{LeFukumotoKoch2024, author = {Le, Thi Thai and Fukumoto, Yasuhide and Koch, Thorsten}, title = {Linear stability of a simple shear layer between two parallel streams in a shallow water flow}, volume = {493}, journal = {Physics Letters A}, publisher = {Elservier}, doi = {10.1016/j.physleta.2023.129264}, year = {2024}, abstract = {The stability of shear layers in fluid flows is a crucial factor in forming vortices and jets and plays a fundamental role in the development of turbulence. Such shear layer instabilities are ubiquitous in natural phenomena, such as atmospheric and oceanic flows, contributing to the formation of weather systems and predicting tsunamis. This study specifically focuses on the stability of a shear layer sandwiched between two semi-infinite layers within a two-dimensional flow. The velocity profile of the shear layer is assumed to be linearly dependent on the vertical coordinate, while the velocity of the other layers remains uniform with differing strengths. The effect of viscosity and surface tension is ignored to simplify the analysis. The shallow water equations are used to analyze the interface stability of the shear layer, and the resulting dispersion relation between wave frequency and other wave characteristics is obtained. This relation incorporates Whittaker functions and their first derivatives and is used to derive appropriate limits corresponding to various physical conditions. Our study thus contributes to a deeper understanding of the stability of shear layers and their implications for natural phenomena.}, language = {en} }