Fluid Mechanics Research Articles

Painlevé analysis, auto-Bäcklund transformations, bilinear form and analytic solutions on some nonzero backgrounds for a $$(2{+}1)$$-dimensional generalized nonlinear evolution system in fluid mechanics and plasma physics

Painlevé analysis, auto-Bäcklund transformations, bilinear form and analytic solutions on some nonzero backgrounds for a $$(2{+}1)$$-dimensional generalized nonlinear evolution system in fluid mechanics and plasma physics

A hard sphere model for single-file water transport across biological membranes.

We use Gürsey's statistical mechanics of a one-dimensional fluid to find a formula for the ratio in the transport of hard spheres across a membrane through a narrow channel that can accommodate molecular movement only in single file. is the membrane permeability for osmotic flow and the permeability for exchange across the membrane in the absence of osmotic flow. The deviation of the ratio from unity indicates the degree of cooperative transport relative to ordinary diffusion of independent molecules. In contrast to an early idea that must be equal to the number of molecules in the channel, regardless of the physical nature of the interactions among the molecules, we find a functional dependence on the fractional occupancy of the length of the channel by the hard spheres. We also attempt a random walk calculation for individually, which gives a result for as well when combined with the ratio.

Research on the Pressure Distribution Law of Synchronous Grouting in Shield Tunnels and the Force on Segments

The pressure distribution and the force on tunnel segments of synchronous grouting in the shield tail gap channel of shield tunnels are key to controlling the stability and surface settlement of the strata surrounding such tunnels. Based on the basic principles of fluid mechanics and the limit equilibrium method, this study establishes a mathematical model of synchronous grouting in shield tunnels, derives the expressions of the grouting pressure and the force on tunnel segments in the shield tail gap channel, and verifies them using an engineering case study. Studies have shown that the force on tunnel segments and the speed of shield excavation are increasing. An excessive shield excavation speed will cause the load on tunnel segments to increase, which exacerbates the uneven distribution of the grouting pressure. The force on tunnel segments and the grouting pressure also have a positive relationship with the thickness of the shield tail gap, but the impact is limited to a certain range. With an increase in the tunnel radius, the number of grouting holes should be appropriately increased to balance the water and soil pressure in the surrounding strata. These research results can provide a theoretical reference for the design of synchronous grouting for shield tunnels in the future.

A Mini-Review of Recent Developments in Plenoptic Background-Oriented Schlieren Technology for Flow Dynamics Measurement

To uncover the underlying fluid mechanisms, it is crucial to explore imaging techniques for high-resolution and large-scale three-dimensional (3D) measurements of the flow field. Plenoptic background-oriented schlieren (Plenoptic BOS), an emerging volumetric method in recent years, has demonstrated being able to resolve volumetric flow dynamics with a single plenoptic camera. The focus-stack-based plenoptic BOS system can qualitatively infer the position of the density gradient in 3D space based on the relative sharpness of the refocused BOS image. Plenoptic BOS systems based on tomography or specular enhancement techniques are realized for use in high-fidelity 3D flow measurements due to the increased number of acquisition views. Here, we first review the fundamentals of plenoptic BOS, and then discuss the system configuration and typical application of single-view and multi-view plenoptic BOS. We also discuss the related challenges and outlook on the potential development of plenoptic BOS in the future.

Innovative flight control explanation and demonstration: bridging theory and practice in secondary education

How do airplanes turn, pitch, and roll? This fundamental question about airplane control captivates many pupils. Offering a comprehensible explanation to secondary school students is challenging due to the complex nature of fluid dynamics and mechanics. In this paper, we provide an accessible explanation of flight control principles, supported by carefully designed illustrations. Furthermore, we address the gap in educational resources by introducing a novel indoor demonstration apparatus. This design employs universal joints and remote-controlled model airplanes to visually demonstrate the principles of airplane control, particularly focusing on the maneuvers of turning, pitching, and rolling. This method is cost-effective, straightforward to implement, and offers students and aviation enthusiasts a highly intuitive and engaging learning experience.

Anthropogenic Impacts in the Lower Stratosphere: Scale Invariant Analysis

Aircraft and rockets entered the lower stratosphere on a regular basis during World War II and have done so in increasing numbers to the present. Atmospheric testing of nuclear weapons saw radioactive isotopes in the stratosphere. Rocket launches of orbiters are projected to increase substantially in the near future. The burnup of orbiters has left signatures in the aerosol. There are proposals to attenuate incoming solar radiation by deliberate injection of artificial aerosols into the stratosphere to “geoengineer” cooling trends in surface temperature, with the aim of countering the heating effects of infrared active gases. These gases are mainly carbon dioxide from fossil burning, with additional contributions from methane, chlorofluorocarbons, nitrous oxide and the accompanying positive feedback from increasing water vapor. Residence times as a function of altitude above the tropopause are critical. The analysis of in situ data is performed using statistical multifractal techniques and combined with remotely sensed and modeled results to examine the classical radiation–photochemistry–fluid mechanics interaction that determines the composition and dynamics of the lower stratosphere. It is critical in assessing anthropogenic effects. It is argued that progress in predictive ability is driven by the continued generation of new and quantitative observations in the laboratory and the atmosphere.

Experimental and Theoretical Insights into Interfacial Properties of 2D Materials for Selective Water Transport Membranes: A Critical Review.

Interfacial properties, such as wettability and friction, play critical roles in nanofluidics and desalination. Understanding the interfacial properties of two-dimensional (2D) materials is crucial in these applications due to the close interaction between liquids and the solid surface. The most important interfacial properties of a solid surface include the water contact angle, which quantifies the extent of interactions between the surface and water, and the water slip length, which determines how much faster water can flow on the surface beyond the predictions of continuum fluid mechanics. This Review seeks to elucidate the mechanism that governs the interfacial properties of diverse 2D materials, including transition metal dichalcogenides (e.g., MoS2), graphene, and hexagonal boron nitride (hBN). Our work consolidates existing experimental and computational insights into 2D material synthesis and modeling and explores their interfacial properties for desalination. We investigated the capabilities of density functional theory and molecular dynamics simulations in analyzing the interfacial properties of 2D materials. Specifically, we highlight how MD simulations have revolutionized our understanding of these properties, paving the way for their effective application in desalination. This Review of the synthesis and interfacial properties of 2D materials unlocks opportunities for further advancement and optimization in desalination.

System Identification Using Self-Adaptive Filtering Applied to Second-Order Gradient Materials

For many engineering applications, it is sufficient to use the concept of simple materials. However, higher gradients of the kinematic variables are taken into account to model materials with internal length scales as well as to describe localization effects using gradient theories in finite plasticity or fluid mechanics. In many approaches, length scale parameters have been introduced that are related to a specific micro structure. An alternative approach is possible, if a thermodynamically consistent framework is used for material modeling, as shown in the present contribution. However, even if sophisticated and thermodynamically consistent material models can be established, there are still not yet standard experiments to determine higher order material constants. In order to contribute to this ongoing discussion, system identification based on the method of self-adaptive filtering is proposed in this paper. To evaluate the effectiveness of this approach, it has been applied to second-order gradient materials considering longitudinal vibrations. Based on thermodynamically consistent models that have been solved numerically, it has been possible to prove that system identification based on self-adaptive filtering can be used effectively for both narrow-band and broadband signals in the field of second-order gradient materials. It has also been found that the differences identified for simple materials and gradient materials allow for condition monitoring and detection of gradient effects in the material behavior.

Mechanics of blood flow through narrow artery using Prandtl viscoelastic model

BackgroundThe mechanics of blood flow via converging diverging conduits is an intriguing phenomenon that involves multiple fundamental principles of fluid dynamics. Blood arteries can diverge, which means they expand, or converge, which means they contract down. This specific structure is essential for controlling blood flow and preserving adequate circulation across the body. The theory of fluid mechanics is significant concept related to blood flow along converging/divergent channels. Elevated shear strains near the narrower artery throat can stimulate platelets, causing thrombosis that can completely or partially stop blood supply to the human brain or heart. This communication addresses the blood flow in convergent and diverging artery using fundamental concept of fluid mechanics. The Prandtl fluid model is considered as a blood, because of its viscoelastic nature. The influence of heat source, frictional dissipations and a chemical reaction are included. MethodsThe Jaffrey-Hamel flow in a converging and diverging conduits is generalized to Prandtl fluid model considering the purely radial flow through cylindrical pipe like artery with an arbitrary cross section. The governing equations are solved computationally using the Runge–Kutta-Fehlberg (RKF-4) method. Significant findingThe rheological parameters ε and δ of blood show opposite tendencies for blood circulation. The Brownian and thermophoresis parameters has a significant effect on heat and mass transport rate. The presence of slip (semi blockage) produces flow reversal and higher drag forces at the arterial wall. Significant flow dynamics and heat-mass transport was reveled for diverging (wider) artery β > 0. The non-uniform heat source show similar trends for thermal profile and heat transfer rate.

Correct Use of Oscillating-Cup Viscometers for High-Temperature Absolute Measurements of Newtonian Melts

Oscillating-body viscometers have been used in the past to measure, in an absolute way, the viscosity of molten materials at high temperatures, from salts, metals, alloys, and semiconductors. However, the simultaneous use of basic or incomplete mathematical models, to mimic the experiment, and less careful engineering solutions for the design and operation of the instruments, led in the past to high discrepancies between the data obtained in several laboratories. This was caused by the incorrect use of the method’s theory, less accurate solutions of the complex solutions, that involve solid state and fluid mechanics, and unreal instrument design. From these types of viscometers, oscillating-cup instruments have had the most success in measuring viscosity at high temperatures, and they will be the object of this paper. It was written as a resource for workers interested in transport properties of materials when considering its use for the absolute measurement of fluids viscosity in their work, or in judging the results of others' work when comparing data with their own. The paper starts with the most accurate theory of the method’s description, followed by a discussion of its validity, application to instrument design, and consequent operation. Several constraints were identified and recommendations were made to minimize the effects of failing to satisfy them. Finally, a discussion about the uncertainty budget calculations for a real experiment is made. If all these points are followed in the design and operation of the instrument, results in global uncertainties Ur(η) between 0.02 and 0.04 are possible to obtain, up to high temperatures. If these constraints are not satisfied, erroneous measurements can be made, making comparisons and quality assessment difficult.

An alternative approach to solenoidal Lipschitz truncation

In this work, we present an alternative approach to obtain a solenoidal Lipschitz truncation result in the spirit of D. Breit, L. Diening and M. Fuchs [Solenoidal Lipschitz truncation and applications in fluid mechanics. J. Differ. Equ. 253 (2012), 1910–1942.]. More precisely, the goal of the truncation is to modify a function $u \in W^{1,p}(\mathbb {R}^N;\mathbb {R}^N)$ that satisfies the additional constraint $\operatorname {div} u=0$ , such that its modification $\tilde {u}$ is Lipschitz continuous and divergence-free. This approach is different to the approaches outlined in the aforementioned work and D. Breit, L. Diening and S. Schwarzacher [Solenoidal Lipschitz truncation for parabolic PDEs. Math. Models Methods Appl. Sci. 23 (2013), 2671–2700, Section 4] and is able to obtain the rather strong bound on the difference between $u$ and $\tilde {u}$ from the former article. Finally, we outline how the approach pursued in this work may be generalized to closed differential forms.

Numerical study of a synergistic hybrid energy harvesting system for bladeless wind turbines

Using energy of the fluid flow over an oscillating vertically-mounted flexible cylinder, as a representative configuration of bladeless wind turbines (BWTs), has recently attracted wide attention in the fluid mechanics community. In this paper, the fluid–structure interactions of a novel BWT-based hybrid piezo-electromagnetic energy harvesting system have been numerically studied in the vortex-induced-vibration (VIV) lock-in region by using the Reynolds Averaged Navier-Stokes (RANS) equations with the SST k-ω turbulence model. It is found that by implementing the electromagnetic (EMT) and/or piezoelectric (PVDF) transducers, the lock-in region becomes wider (up to 33% for the hybrid system) while being shifted to the higher Reynolds number (Re) range. Also, the dimensionless BWT cross-flow tip displacement amplitude (Yamp∗) is seen to reduce about 20%, 70%, and 70% by using the single-alone EMT-based, single-along piezo-based, and the hybrid harvester, respectively, which can potentially lead to substantial improvements in the fatigue life of the system Furthermore, the synergetic action of the hybrid system is observed to cause an overall increase in the harvested energy levels besides broadening of the associated range, as each of energy harvesting components appears to produce higher output power as compared to the respective single-alone system. In other words, up to 260% increase (100% increase) in the overall harvested energy level and up to 300% increase (60% increase) in the harvestable Re range with respect to the single-alone piezo-based (EMT-based) system are obtained, in which about 50% (about 10%) synergetic effects can be associated with the EMT- and piezo-based transducers, respectively.

The principle of minimum pressure gradient: An alternative basis for physics-informed learning of incompressible fluid mechanics

Recent advances in the application of physics-informed learning in the field of fluid mechanics have been predominantly grounded in the Newtonian framework, primarily leveraging Navier–Stokes equations or one of their various derivatives to train a neural network. Here, we propose an alternative approach based on variational methods. The proposed approach uses the principle of minimum pressure gradient combined with the continuity constraint to train a neural network and predict the flow field in incompressible fluids. We describe the underlying principles of the proposed approach, then use a demonstrative example to illustrate its implementation, and show that it reduces the computational time per training epoch when compared to the conventional approach.

Solitons, nonlinear wave transitions and characteristics of quasi-periodic waves for a (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation in fluid mechanics and plasma physics

A (3+1)-dimensional generalized Calogero–Bogoyavlenskii–Schiff equation describing many nonlinear phenomena in fluid dynamics and plasma physics is considered. The N-solitons and breathers are obtained by basing on its Hirota’s bilinear form and taking the complex conjugate condition on parameters of N-solitons. What is more, breathers can be transformed into a series of nonlinear localized waves by the mechanism of breather transformation. Then through the multi-dimensional Riemann-theta function and the bilinear method, the high-dimensional complex three-periodic wave solutions are constructed systematically, which are the generalization of one-periodic wave and two-periodic wave solutions. By a limiting procedure, the asymptotic relations between the quasi-periodic waves and solitons are strictly established. Additionally, a novel analytical method of characteristic line is introduced to analyze statistically the dynamical characteristics of the quasi-periodic waves. The analytical method employed in this paper can be further extended to investigate the other complex high-dimensional nonlinear integrable equations.

The turbulent jet in the scale-relativity framework

The turbulent jet plays an important role in fluid mechanics since it is a prototype of free turbulent flow which presents many unsolved problems, among which the absence of closure of the governing equations. Despite the chaotic nature of turbulence, it is characterized by the existence of many universal structures, in particular dimensionless invariants such as its opening angle or the correlation coefficient of velocities. After having given new exact solutions of the Reynolds Averaged Navier–Stokes equations (RANS), we suggest a solution to this puzzle in the scale-relativity framework. In this theory, the time derivative of the Navier–Stokes equations is integrated in terms of a macroscopic Schrödinger equation acting in velocity-space. This equation involves a constant ℏv which can be identified with the energy dissipation rate, while the pressure gradient manifests itself as a quantum harmonic oscillator (QHO) potential. The squared modulus of its solutions yields the probability density function (PDF) of velocities. The Reynolds stresses can then be derived from this PDF, so that the closure problem is solved in this case. This allows us to obtain a theoretical prediction for the turbulent intensity radial profile (and therefore for the pressure) which agrees with the experimental data. The ratio of axial over radial velocity fluctuations is found to be R=1.3–1.4 from QHO properties, in good agreement with its experimental values; we theoretically predict a jet opening angle α=1/2R3 accounting for its universal value ≈1/5; the mean ratio of turbulent intensity amplitudes over jet centerline axial velocity is predicted to be X=19/80, in good agreement with its universally measured value ≈1/4; from these parameters we derive possible values of the radial turbulent intensity amplitude μ=0.19–0.22 consistent with experiments; finally, we find a correlation coefficient of velocities ρ=1/R3=2 α, suggesting an explanation for the universal value ≈0.4 observed for the turbulent jet and for all free shear flows.

Grasping the behavior of magnetorheological fluids in gradient pinch mode via microscopic imaging

Magnetorheological (MR) fluids are suspensions of micrometer-sized ferromagnetic particles in a carrier fluid, which react to magnetic fields. The fluids can be operated in several fundamental modes. Contrary to the other modes, the rheology and microstructure formation of the MR fluid in the gradient pinch mode have been studied to a far lesser extent. The magnetic field distribution in the flow channel is intentionally made non-uniform. It is hypothesized that the Venturi-like contraction is achieved via fluid property changes, leading to a unique behavior and the presence of a pseudo-orifice. The main goal is to investigate the presence of the Venturi-like contraction effect in the fluid by means of optical imaging and hydraulic measurements. To accomplish the goal, a unique test rig has been developed including a fluorescence microscope and MR valve prototype. The Venturi-like contraction hypothesis was confirmed. The results indicate that the effective flow channel size decreases by 92% at the maximum magnetic flux applied. This has a direct impact on the flow characteristics of the MR valve. The variation of the pressure–flow rate curve slope with magnetic field was demonstrated. The results provide valuable information for understanding the rheology and microstructure formation mechanism in MR fluids in the pinch mode.

Computational fluid dynamics method for determining the rotational diffusion coefficient of cells

This work presents a straightforward computational method to estimate the rotational diffusion coefficient (Dr) of cells and particles of various sizes using the continuum fluid mechanics theory. We calculate the torque (Γ) for cells and particles immersed in fluids to find the mobility coefficient μ and then obtain the Dr by substituting Γ in the Einstein relation. Geometries are constructed using triangular mesh, and the model is solved with computational fluid dynamics techniques. This method is less intensive and more efficient than the widely used models. We simulate eight different particle geometries and compare the results with previous literature.

Investigating the Mechanisms of Intradermal Injection for Easier "Skin Booster" Treatment: A Fluid Mechanics Approach to Determine Optimal Delivery Method.

The use of "skin boosters" for rejuvenating aged skin is widely used. However, the accurate injection of the skin booster into the dermal layer remains a challenge due to the density of the dermis. The purpose of this study was to investigate the optimal mechanical variables of delivery that enabled correct targeting of the product to the dermis for optimal results. We investigated the impact of mechanical variables (syringe diameter, needle diameter and length, and viscosity of the skin booster) on the force required for intradermal injection in porcine skin. The correlation between these variables and the injection force was examined as well. The results show that smaller syringe diameters, larger needle diameters, shorter needle lengths, and lower viscosity of the skin boosters reduce the injection force needed for intradermal injections. During the administration of skin booster injections, clinicians should take into account optimal conditions that facilitate intradermal injections, thus maximizing rejuvenating outcomes. Furthermore, manufacturers of skin boosters should formulate the products with decreased viscosity and provide the product in conjunction with appropriate needles and syringes, designed to optimize ease of injection.

Uncertainty quantification of the impact of peripheral arterial disease on abdominal aortic aneurysms in blood flow simulations.

Peripheral arterial disease (PAD) and abdominal aortic aneurysms (AAAs) often coexist and pose significant risks of mortality, yet their mutual interactions remain largely unexplored. Here, we introduce a fluid mechanics model designed to simulate the haemodynamic impact of PAD on AAA-associated risk factors. Our focus lies on quantifying the uncertainty inherent in controlling the flow rates within PAD-affected vessels and predicting AAA risk factors derived from wall shear stress. We perform a sensitivity analysis on nine critical model parameters through simulations of three-dimensional blood flow within a comprehensive arterial geometry. Our results show effective control of the flow rates using two-element Windkessel models, although specific outlets need attention. Quantities of interest like endothelial cell activation potential (ECAP) and relative residence time are instructive for identifying high-risk regions, with ECAP showing greater reliability and adaptability. Our analysis reveals that the uncertainty in the quantities of interest is 187% of that of the input parameters. Notably, parameters governing the amplitude and frequency of the inlet velocity exert the strongest influence on the risk factors' variability and warrant precise determination. This study forms the foundation for patient-specific simulations involving PAD and AAAs which should ultimately improve patient outcomes and reduce associated mortality rates.

Analysis of Fluid Pressure Drop through a Globe Valve using Computational Fluid Dynamics and Statistical Techniques

Fluid mechanics plays a crucial role in everyday life, enabling the selection of accessories, materials, and various components essential for a system through which fluid flows. Pressure drop stands out as one of the most relevant factors in the design of fluid flow systems. However, analytical and experimental physical methods can increase these analyses' costs and time. Hence, in this study, statistical tools are employed to carry out specific experiments supported by numerical fluid simulation, aiming to comprehend the pressure drop behavior in a fluid as it passes through a globe valve. This valve, in turn, possesses distinct operating and manufacturing characteristics. The methods employed encompass a complete factorial system of response surface as support to construct the experimental design path through computational fluid dynamics. Among the key findings, it is demonstrated that, for systems with relatively low flow rates, the valve opening percentage does not exhibit a significant relationship with fluid pressure drop. Conversely, significant effects are observed for systems with relatively high flow rates regarding the valve opening percentage and pressure drop, reaching values of up to 73% pressure drop in this study. It can be inferred that the integration of statistical experimental design techniques and computational fluid dynamics constitutes a valuable resource for studying the pressure drop of a fluid passing through a system.