Fluids, Volume 5, Issue 1 (March 2020) – 40 articles

The Langevin equations (LE) and the Fokker–Planck (FP) equations are widely used to describe fluid behavior based on coarse-grained approximations of microstructure evolution. In this manuscript, we describe the relation between LE and FP as related to particle motion within a fluid. The manuscript introduces undergraduate students to two LEs, their corresponding FP equations, and their solutions and physical interpretation. Full article

Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models. Full article

Many organisms achieve locomotion via reciprocal motions. This paper presents the dynamic analysis and design optimization of a vibratory swimmer with asymmetric drag forces and fluid added mass. The swimmer consists of a floating body with an oscillatory mass inside. One-dimensional oscillations of the mass cause the body to oscillate with the same frequency as the mass. An asymmetric rigid fin attached to the bottom of the body generates asymmetric hydrodynamic forces, which drive the swimmer either backward or forward on average, depending on the orientation of the fin. The equation of motion of the system is a time-periodic, piecewise-smooth differential equation. We use simulations to determine the hydrodynamic forces acting on the fin and averaging techniques to determine the dynamic response of the swimmer. The analytical results are found to be in good agreement with vibratory swimmer prototype experiments. We found that the average unidirectional speed of the swimmer is optimized if the ratio of the forward and backward drag coefficients is minimized. The analysis presented here can aid in the design and optimization of bio-inspired and biomimetic robotic swimmers. A magnetically controlled microscale vibratory swimmer like the one described here could have applications in targeted drug delivery. Full article

The present studies address feeding of plankton in turbulent environments, discussed by a comparison of analytical results and field data. Various models for predator-prey encounters and capture probabilities are reviewed. Generalized forms for encounter rates and capture probabilities in turbulent environments are proposed. The analysis emphasizes ambush predators, exemplified by cod larvae Gadus morhua L. in the start-feeding phase (stage 7 larvae) collected in shallow waters near Lofoten, Norway. During this campaign, data were obtained at four sites with strongly turbulent conditions induced by tidal currents and long-wave swells, and one site where the turbulence had a lower level in comparison. The guts of the selected cod larvae were examined in order to determine the number of nauplii ingested. Analytically obtained probability densities for the gut content were compared with observations and the results used for estimating the rate of capture of the nauplii. This capture rate was then compared with analytical results using also data for the surroundings, such as measured prey densities and turbulence conditions, as quantified by the specific energy dissipation rate. Different from earlier studies, the presented data include conditions where the turbulence exceeds the level for optimal larval encounter-capture rates. Full article

In this manuscript, an automated framework dedicated to design space exploration and design optimization studies is presented. The framework integrates a set of numerical simulation, computer-aided design, numerical optimization, and data analytics tools using scripting capabilities. The tools used are open-source and freeware, and can be deployed on any platform. The main feature of the proposed methodology is the use of a cloud-based parametrical computer-aided design application, which allows the user to change any parametric variable defined in the solid model. We demonstrate the capabilities and flexibility of the framework using computational fluid dynamics applications; however, the same workflow can be used with any numerical simulation tool (e.g., a structural solver or a spread-sheet) that is able to interact via a command-line interface or using scripting languages. We conduct design space exploration and design optimization studies using quantitative and qualitative metrics, and, to reduce the high computing times and computational resources intrinsic to these kinds of studies, concurrent simulations and surrogate-based optimization are used. Full article

Through the combination of passive and active load alleviation techniques, this paper presents the design, optimization, manufacturing, and update of a flexible composite wind tunnel model. In a first step, starting from the specification of an adequate wing and trailing edge flap geometry, passive, static aeroelastic stiffness optimizations for various objective functions have been performed. The second optimization step comprised a discretization of the continuous stiffness distributions, resulting in manufacturable stacking sequences. In order to determine which of the objective functions investigated in the passive structural optimization most efficiently complemented the projected active control schemes, the condensed modal finite element models were integrated in an aeroelastic model, involving a dedicated gust load alleviation controller. The most promising design was selected for manufacturing. The finite element representation could be updated to conform to the measured eigenfrequencies, based on the dynamic identification of the model. Eventually, a wind tunnel test campaign was conducted in November 2018 and results have been examined in separate reports. Full article

Aiming at the experimental test of the body freedom flutter for modern high aspect ratio flexible flying wing, this paper conducts a body freedom flutter wind tunnel test on a full-span flying wing flutter model. The research content is summarized as follows: (1) The full-span finite element model and aeroelastic model of an unmanned aerial vehicle for body freedom flutter wind tunnel test are established, and the structural dynamics and flutter characteristics of this vehicle are obtained through theoretical analysis. (2) Based on the preliminary theoretical analysis results, the design and manufacturing of this vehicle are completed, and the structural dynamic characteristics of the vehicle are identified through ground vibration test. Finally, the theoretical analysis model is updated and the corresponding flutter characteristics are obtained. (3) A novel quasi-free flying suspension system capable of releasing pitch, plunge and yaw degrees of freedom is designed and implemented in the wind tunnel flutter test. The influence of the nose mass balance on the flutter results is explored. The study shows that: (1) The test vehicle can exhibit body freedom flutter at low airspeeds, and the obtained flutter speed and damping characteristics are favorable for conducting the body freedom flutter wind tunnel test. (2) The designed suspension system can effectively release the degrees of freedom of pitch, plunge, and yaw. The flutter speed measured in the wind tunnel test is 9.72 m/s, and the flutter frequency is 2.18 Hz, which agree well with the theoretical results (with flutter speed of 9.49 m/s and flutter frequency of 2.03 Hz). (3) With the increasing of the mass balance at the nose, critical speed of body freedom flutter rises up and the flutter frequency gradually decreases, which also agree well with corresponding theoretical results. Full article

Suction feeding is a well-understood feeding mode among macroscopic aquatic organisms. The little we know about small suction feeders from larval fish suggests that small suction feeders are not effective. Yet bladderworts, an aquatic carnivorous plant with microscopic underwater traps, have strong suction performances despite having the same mouth size as that of fish larvae. Previous experimental studies of bladderwort suction feeding have focused on the solid mechanics of the trap door’s opening mechanism rather than the mechanics of fluid flow. As flows are difficult to study in small suction feeders due to their small size and brief event durations, we combine flow visualization on bladderwort traps with measurements on a mechanical, dynamically scaled model of a suction feeder. We find that bladderwort traps generate flows that are more similar to the inertia-dominated flows of adult fish than the viscosity-dominated flows of larval fish. Our data further suggest that axial flow transects through suction flow fields, often used in biological studies to characterize suction flows, are less diagnostic of the relative contribution of inertia versus viscosity than transverse transects. Full article

This research explores the effects of different spans of two columns of tandem piers on the characteristics of x-velocity near the river bed based on computational fluid dynamics (CFD) simulations. With a span shorter than 27.5D (D is the diameter of piers), the shape and the lateral range of the x-velocity increases with the increase of distance downwards the x-direction. For the area between the tandem piers and the wall, the V_Ri/V_R1 (the ratio of the x-velocity at the i-th row to the x-velocity of the first row in each model) near the wall increases up to 1.26. For the area between the two columns of tandem piers, the profile of V_Ri/V_R1 changes from a “∩-shape” to an “M-shape” in each model. R_AVC (average velocity change ratio) of different spans increases gradually and tends to be stable with the increases of the span. The largest R_AVC is about −17.66% with a span of 0.52 m. The R_MV (the ratio of the maximum x-velocity among piers in each row in different models to the maximum x-velocity of the two piers arranged side by side) of piers in the first row of different models is around 0.95. The R_MV becomes 0.82 at the second pier in each model when the span is shorter than 27.5D, and increases to 0.91 if the span is longer than 27.5D. If the span is longer than 27.5D, the R_MV of different piers are close to each other from the 2nd pier to the last one. Full article

The continuous adjoint approach is a technique for calculating the sensitivity of a flow to changes in input parameters, most commonly changes of geometry. Here we present for the first time the mathematical derivation of the adjoint system for multiphase flow modeled by the commonly used drift flux equations, together with the adjoint boundary conditions necessary to solve a generic multiphase flow problem. The objective function is defined for such a system, and specific examples derived for commonly used settling velocity formulations such as the Takacs and Dahl models. We also discuss the use of these equations for a complete optimisation process. Full article

Bone grafts represent a multibillion-dollar industry, with over a million grafts occurring each year. Common graft types are associated with issues such as donor site morbidity in autologous grafts and immunological response in allogenic grafts. Bone-tissue-engineered constructs are a logical approach to combat the issues commonly encountered with these bone grafting techniques. When creating bone-tissue-engineered constructs, monitoring systems are required to determine construct characteristics, such as cellularity and cell type. This study aims to expand on the current predictive metrics for these characteristics, specifically analyzing the effects of media flow rate on oxygen uptake rates (OURs) of mesenchymal stem cells seeded on poly(L-lactic acid) (PLLA) scaffolds cultured in a flow perfusion bioreactor. To do this, oxygen consumption rates were measured for cell/scaffold constructs at varying flow rates ranging from 150 to 750 microliters per minute. Residence time analyses were performed for this bioreactor at these flow rates. Average observed oxygen uptake rates of stem cells in perfusion bioreactors were shown to increase with increased oxygen availability at higher flow rates. The residence time analysis helped identify potential pitfalls in current bioreactor designs, such as the presence of channeling. Furthermore, this analysis shows that oxygen uptake rates have a strong linear correlation with residence times of media in the bioreactor setup, where cells were seen to exhibit a maximum oxygen uptake rate of 3 picomoles O₂/hr/cell. Full article

This review paper provides an overview of the literature for topology optimisation of fluid-based problems, starting with the seminal works on the subject and ending with a snapshot of the state of the art of this rapidly developing field. “Fluid-based problems” are defined as problems where at least one governing equation for fluid flow is solved and the fluid–solid interface is optimised. In addition to fluid flow, any number of additional physics can be solved, such as species transport, heat transfer and mechanics. The review covers 186 papers from 2003 up to and including January 2020, which are sorted into five main groups: pure fluid flow; species transport; conjugate heat transfer; fluid–structure interaction; microstructure and porous media. Each paper is very briefly introduced in chronological order of publication. A quantititive analysis is presented with statistics covering the development of the field and presenting the distribution over subgroups. Recommendations for focus areas of future research are made based on the extensive literature review, the quantitative analysis, as well as the authors’ personal experience and opinions. Since the vast majority of papers treat steady-state laminar pure fluid flow, with no recent major advancements, it is recommended that future research focuses on more complex problems, e.g., transient and turbulent flow. Full article

Computational Fluid Dynamics (CFD) models are being rapidly integrated into applications across all sciences and engineering. CFD harnesses the power of computers to solve the equations of fluid dynamics, which otherwise cannot be solved analytically except for very particular cases. Numerical solutions can be interpreted through traditional quantitative techniques as well as visually through qualitative snapshots of the flow data. As pictures are worth a thousand words, in many cases such visualizations are invaluable for understanding the fluid system. Unfortunately, vast mathematical knowledge is required to develop one’s own CFD software and commercial software options are expensive and thereby may be inaccessible to many potential practitioners. To that extent, CFD materials specifically designed for undergraduate education are limited. Here we provide an open-source repository, which contains numerous popular fluid solvers in $2D$ (projection, spectral, and Lattice Boltzmann), with full implementations in both MATLAB and Python3. All output data is saved in the $.vtk$ format, which can be visualized (and analyzed) with open-source visualization tools, such as VisIt or ParaView. Beyond the code, we also provide teaching resources, such as tutorials, flow snapshots, measurements, videos, and slides to streamline use of the software. Full article

This study presents the measured densities and viscosities of three ternary aqueous mixtures of tertiary and primary amines. The tertiary amines of n-methyldiethanolamine (MDEA), dimethylethanolamine (DMEA), diethylethanolamine (DEEA), and the primary amine monoethanolamine (MEA) at different concentrations (mass%) were mixed to prepare the liquid mixtures. The excess molar volume VE of the mixtures was analyzed using measured densities to acquire a better understanding of the molecular packing and intermolecular interactions in the mixtures. The excess free energy of activation ∆GE* and excess entropy of activation ∆SE* for viscous flow were determined from the measured viscosities by implementing the theory of rate processes of Eyring. Correlations based on the Redlich–Kister type polynomial were adopted to correlate the excess properties VE and ∆GE* as a function of the amine mole fraction and temperature. The results showed that the correlations were able to represent the measured data with satisfactory accuracies for engineering calculations. Full article

Turbulence modeling has been always a challenge, given the degree of underlying spatial and temporal complexity. In this paper, we propose the use of a partitioned reduced order modeling (ROM) approach for efficient and effective approximation of turbulent flows. A piecewise linear subspace is tailored to capture the fine flow details in addition to the larger scales. We test the partitioned ROM for a decaying two-dimensional (2D) turbulent flow, known as 2D Kraichnan turbulence. The flow is initiated using an array of random vortices, corresponding to an arbitrary energy spectrum. We show that partitioning produces more accurate and stable results than standard ROM based on a global application of modal decomposition techniques. We also demonstrate the predictive capability of partitioned ROM through an energy spectrum analysis, where the recovered energy spectrum significantly converges to the full order model’s statistics with increased partitioning. Although the proposed approach incurs increased memory requirements to store the local basis functions for each partition, we emphasize that it permits the construction of more compact ROMs (i.e., of smaller dimension) with comparable accuracy, which in turn significantly reduces the online computational burden. Therefore, we consider that partitioning acts as a converter which reduces the cost of online deployment at the expense of offline and memory costs. Finally, we investigate the application of closure modeling to account for the effects of modal truncation on ROM dynamics. We illustrate that closure techniques can help to stabilize the results in the inertial range, but over-stabilization might take place in the dissipative range. Full article

The placement of a cylindrical body in a flow alters the velocity and pressure fields resulting in a local increase in the flow speed near the body. This interaction is of interest as wind turbine rotor blades could be placed in the area of increased wind speed to enhance energy harvesting. In this work the aerodynamic performance of two short aspect ratio (AR = 0.93) cylindrical bodies was evaluated for potential use in “accelerated wind” applications. The first cylinder was smooth with a constant diameter. The diameter of the second cylinder varied periodically along the span forming channels, or corrugations, where wind turbine blades could be placed. Experiments were performed for Reynolds numbers ranging from 1 × 10⁵ to 9 × 10⁵. Pressure distributions showed that the smooth cylinder had lower minimum pressure coefficients and delayed separation compared to the corrugated cylinder. Velocity profiles showed that the corrugated cylinder had lower peak speeds, a less uniform profile, and lower kinetic energy flux when compared to the smooth cylinder. It was concluded that the smooth cylinder had significantly better potential performance in accelerated wind applications than the corrugated cylinder. Full article

Various organisms such as crustaceans use their appendages for locomotion. If they are close to a confining boundary then viscous as opposed to inertial effects can play a central role in governing the dynamics. To study the minimal ingredients needed for swimming without inertia, we built an experimental system featuring a robot equipped with a pair of rigid slender arms with negligible inertia. Our results show that directing the arms to oscillate about the same time-averaged orientation produces no net displacement of the robot each cycle, regardless of any phase delay between the oscillating arms. The robot is able to swim if the arms oscillate asynchronously around distinct orientations. The measured displacement over time matches well with a mathematical model based on slender-body theory for Stokes flow. Near a confining boundary, the robot with no net displacement every cycle showed similar behavior, while the swimming robot increased in speed closer to the boundary. Full article

This study focuses on the utilisation of lab-based activities to enhance the learning experience of engineering students studying water engineering and geosciences courses. Specifically, the use of “floodopoly” as a physical model demonstration in improving the students’ understanding of the relevant processes of flooding, infrastructure scour and sediment transport, and improve retention and performance in simulation of these processes in engineering design courses, is discussed. The effectiveness of lab-based demonstration is explored using a survey assessing the weight of various factors that might influence students’ performance and satisfaction. It reveals how lab-centred learning, overall course success is linked with student motivation and the students’ perception of an inclusive teaching environment. It also explores the effectiveness of the implementation of student-centred and inquiry-guided teaching and various methods of assessment. The analysis and discussion are informed by students’ responses to a specifically designed questionnaire, showing an improvement of the satisfaction rates compared to traditional class-based learning modules. For example, more students (85%) reported that they perceived the lab-based environment as an excellent contribution to their learning experience, while less students (about 57%) were as satisfied for a traditional class-based course delivery. Such findings can be used to improve students’ learning experience by introducing physical model demonstrations, similar to those offered herein. Full article

Nematocysts are stinging organelles used by members of the phylum Cnidaria (e.g., jellyfish, anemones, hydrozoans) for a variety of important functions including capturing prey and defense. Nematocysts are the fastest-known accelerating structures in the animal world. The small scale (microns) coupled with rapid acceleration (in excess of 5 million g) present significant challenges in imaging that prevent detailed descriptions of their kinematics. The immersed boundary method was used to numerically simulate the dynamics of a barb-like structure accelerating a short distance across Reynolds numbers ranging from 0.9–900 towards a passive elastic target in two dimensions. Results indicate that acceleration followed by coasting at lower Reynolds numbers is not sufficient for a nematocyst to reach its target. The nematocyst’s barb-like projectile requires high accelerations in order to transition to the inertial regime and overcome the viscous damping effects normally encountered at small cellular scales. The longer the barb is in the inertial regime, the higher the final velocity of the projectile when it touches its target. We find the size of the target prey does not dramatically affect the barb’s approach for large enough values of the Reynolds number, however longer barbs are able to accelerate a larger amount of surrounding fluid, which in turn allows the barb to remain in the inertial regime for a longer period of time. Since the final velocity is proportional to the force available for piercing the membrane of the prey, high accelerations that allow the system to persist in the inertial regime have implications for the nematocyst’s ability to puncture surfaces such as cellular membranes or even crustacean cuticle. Full article

Nano/microrobotic swimmers have many possible biomedical applications such as drug delivery and micro-manipulation. This paper examines one of the most promising classes of these: rigid magnetic microrobots that are propelled through bulk fluid by rotation induced by a rotating magnetic field. Propulsion corresponds to steadily rotating and translating solutions of the dynamics of such microrobots that co-rotate with the magnetic field. To be observed in experiments and be amenable to steering control, such solutions must also be stable to perturbations. In this paper, we analytically derive a criterion for the stability of such steadily rotating solutions for a microrobot made of soft magnetic materials, which have a magnetization that depends on the applied field. This result generalizes previous stability criteria we obtained for microrobots with a permanent magnetization. Full article

Many industrial processes depend on the wetting of liquids on various surfaces. Understanding the wetting effects due to ultrasonic vibration could provide a means for changing the behavior of liquids on any surface. In previous studies, low-frequency surface vibrations have been used to alter wetting states of droplets by exciting droplet volume modes. While high-frequency (>20 kHz) surface vibration can also cause droplets to wet or spread on a surface, this effect is relatively uncharacterized. In this study, droplets of various liquids with volumes ranging from 2 to 70 µL were vibrated on hydrophobic-coated (FluoroSyl) glass substrates fixed to a piezoelectric transducer at varying amplitudes and at a range of frequencies between 21 and 42 kHz. The conditions for contact line motion were evaluated, and the change in droplet diameter under vibration was measured. Droplets of all tested liquids initially begin to spread out at a similar surface acceleration level. The results show that the increase in diameter is proportional to the maximum acceleration of the surface. Finally, liquid properties and surface roughness may also produce some secondary effects, but droplet volume and excitation frequency do not significantly change the droplet spreading behavior within the parameter range studied. Full article

The objective of this paper is to show how a completely virtual optimization approach is useful to design new geometries in order to improve the performance of industrial components, like valves. The standard approach for optimization of an industrial component, as a valve, is mainly performed with trials and errors and is based on the experience and knowledge of the engineer involved in the study. Unfortunately, this approach is time consuming and often not affordable for the industrial time-to-market. The introduction of computational fluid dynamic (CFD) tools significantly helped reducing time to market; on the other hand, the process to identify the best configuration still depends on the personal sensitivity of the engineer. Here a more general, faster and reliable approach is described, which uses a CFD code directly linked to an optimization tool. CAESES^® associated with SimericsMP+^® allows us to easily study many different geometrical variants and work out a design of experiments (DOE) sequence that gives evidence of the most impactful aspects of a design. Moreover, the result can be further optimized to obtain the best possible solution in terms of the constraints defined. Full article

Permeability is a parameter that measures the resistance that fluid faces when flowing through a porous medium. Usually, this parameter is determined in routine laboratory tests by applying Darcy’s law. Those tests can be complex and time-demanding, and they do not offer a deep understanding of the material internal microstructure. Currently, with the development of new computational technologies, it is possible to simulate fluid flow experiments in computational labs. Determining permeability with this strategy implies solving a homogenization problem, where the determination of the macro parameter relies on the simulation of a fluid flowing through channels created by connected pores present in the material’s internal microstructure. This is a powerful example of the application of fluid mechanics to solve important industrial problems (e.g., material characterization), in which the students can learn basic concepts of fluid flow while practicing the implementation of computer simulations. In addition, it gives the students a concrete opportunity to work with a problem that associates two different scales. In this work, we present an educational code to compute absolute permeability of heterogeneous materials. The program simulates a Stokes flow in the porous media modeled with periodic boundary conditions using finite elements. Lastly, the permeability of a real sample of sandstone, modeled by microcomputed tomography (micro-CT), is obtained. Full article

Micro-swimmers such as spermatozoa are able to efficiently navigate through viscous fluids that contain a sparse network of fibers or other macromolecules. We utilize the Brinkman equation to capture the fluid dynamics of sparse and stationary obstacles that are represented via a single resistance parameter. The method of regularized Brinkmanlets is utilized to solve for the fluid flow and motion of the swimmer in 2-dimensions when assuming the flagellum (tail) propagates a curvature wave. Extending previous studies, we investigate the dynamics of swimming when varying the resistance parameter, head or cell body radius, and preferred beat form parameters. For a single swimmer, we determine that increased swimming speed occurs for a smaller cell body radius and smaller fluid resistance. Progression of swimmers exhibits complex dynamics when considering hydrodynamic interactions; attraction of two swimmers is a robust phenomenon for smaller beat amplitude of the tail and smaller fluid resistance. Wall attraction is also observed, with a longer time scale of wall attraction with a larger resistance parameter. Full article

Densities and viscosities of aqueous monoethanol amine (MEA) and CO₂-loaded aqueous MEA are highly relevant in engineering calculations to perform process design and simulations. Density and viscosity of the aqueous MEA were measured in the temperature range of 293.15 K to 363.15 K with MEA mass fractions ranging from 0.3 to 1.0. Densities of the aqueous MEA were fitted for a density correlation. Eyring’s viscosity model based on absolute rate theory was adopted to determine the excess free energy of activation for viscous flow of aqueous MEA mixtures and was correlated by a Redlich–Kister polynomial. Densities and viscosities of CO₂-loaded MEA solutions were measured in the temperature range of 293.15 K to 353.15 K with MEA mass fractions of 0.3, 0.4 and 0.5. The density correlation used to correlate aqueous MEA was modified to fit CO₂-loaded density data. The free energy of activation for viscous flow for CO₂-loaded aqueous MEA solutions was determined by Eyring’s viscosity model and a correlation was proposed to represent free energy of activation for viscous flow and viscosity. This can be used to evaluate quantitative and qualitative properties in the MEA + H₂O + CO₂ mixture. Full article

In order to ensure stable power exhaust and to protect the walls of fusion reactors, liquid metals that are fed to the wall surface through a capillary porous system (CPS) are considered as alternative plasma-facing components (PFCs). However, operational issues like drop ejection and plasma contamination may arise. In this study, the unsteady flow of a liquid metal inside a single pore of the CPS in the presence of Lorentz forces is investigated. A numerical solution is performed via the finite element methodology coupled with elliptic mesh generation. A critical magnetic number is found (Bond_m = 4.5) below which the flow after a few oscillations reaches a steady state with mild rotational patterns. Above this threshold, the interface exhibits saturated oscillations. As the Lorentz force is further increased, Bond_m > 5.8, a Rayleigh–Taylor instability develops as the interface is accelerated under the influence of the increased magnetic pressure and a finite time singularity is captured. It is conjectured that eventually, drop ejection will take place that will disrupt cohesion of the interface and contaminate the surrounding medium. Finally, the dynamic response of different operating fluids is investigated, e.g., gallium, and the stabilizing effect of increased electrical conductivity and surface tension is demonstrated. Full article

In this paper, the continuous adjoint method is used for the optimization of a static mixing device. The CFD model used is suitable for the flow simulation of the two miscible fluids that enter the device. The formulation of the adjoint equations, which allow the computation of the sensitivity derivatives is briefly demonstrated. A detailed analysis of the geometry parameterization is presented and a set of different parameterization scenarios are investigated. In detail, two different parameterizations are combined into a two-stage optimization algorithm which targets maximum mixture uniformity at the exit of the mixer and minimum total pressure losses. All parameterizations are in conformity with specific manufacturability constraints of the final shape. The non-dominated front of optimal solutions is obtained by using the weighted sum of the two objective functions and executing a set of optimization runs. The effectiveness of the proposed synthetic parameterization schemes is assessed and discussed in detail. Finally, a reduced length mixer is optimized to study the impact of the length of the tube on the device’s performance. Full article