Incompressible Research Articles

Two-Dimensional Surface Periodic Flows of an Incompressible Fluid in Various Models of the Medium

A comparative analysis of the properties of two-dimensional infinitesimal periodic perturbations propagating over the incompressible fluid surface in various representations of the medium density profiles is carried out. Stratified and homogeneous in density viscous or ideal liquids are considered. Calculations are carried out by methods of the theory of singular perturbations. Dispersion relations and dependences of phase and group velocities for surface waves in physically observed variables are given. The change in the meaning of dispersion relations during the transition from ideal liquids to viscous and from homogeneous to stratified is shown. Taking into account the influence of electric charge does not qualitatively change the nature of two-dimensional dispersion relations. An increase in the surface density of the electric charge leads to a decrease in the wavelength at a fixed frequency and has no noticeable effect on the fine structure of the periodic flow.

A Pseudo-Spectral Method for Wall Shear Stress Estimation from Doppler Ultrasound Imaging in Coronary Arteries.

The Wall Shear Stress (WSS) is the component tangential to the boundary of the normal stress tensor in an incompressible fluid, and it has been recognized as a quantity of primary importance in predicting possible adverse events in cardiovascular diseases, in general, and in coronary diseases, in particular. The quantification of the WSS in patient-specific settings can be achieved by performing a Computational Fluid Dynamics (CFD) analysis based on patient geometry, or it can be retrieved by a numerical approximation based on blood flow velocity data, e.g., ultrasound (US) Doppler measurements. This paper presents a novel method for WSS quantification from 2D vector Doppler measurements. Images were obtained through unfocused plane waves and transverse oscillation to acquire both in-plane velocity components. These velocity components were processed using pseudo-spectral differentiation techniques based on Fourier approximations of the derivatives to compute the WSS. Our Pseudo-Spectral Method (PSM) is tested in two vessel phantoms, straight and stenotic, where a steady flow of 15mL/min is applied. The method is successfully validated against CFD simulations and compared against current techniques based on the assumption of a parabolic velocity profile. The PSM accurately detected Wall Shear Stress (WSS) variations in geometries differing from straight cylinders, and is less sensitive to measurement noise. In particular, when using synthetic data (noise free, e.g., generated by CFD) on cylindrical geometries, the Poiseuille-based methods and PSM have comparable accuracy; on the contrary, when using the data retrieved from US measures, the average error of the WSS obtained with the PSM turned out to be 3 to 9 times smaller than that obtained by state-of-the-art methods. The pseudo-spectral approach allows controlling the approximation errors in the presence of noisy data. This gives a more accurate alternative to the present standard and a less computationally expensive choice compared to CFD, which also requires high-quality data to reconstruct the vessel geometry.

Bridging Large Eddy Simulation and Reduced-Order Modeling of Convection-Dominated Flows through Spatial Filtering: Review and Perspectives

Reduced-order models (ROMs) have achieved a lot of success in reducing the computational cost of traditional numerical methods across many disciplines. In fluid dynamics, ROMs have been successful in providing efficient and relatively accurate solutions for the numerical simulation of laminar flows. For convection-dominated (e.g., turbulent) flows, however, standard ROMs generally yield inaccurate results, usually affected by spurious oscillations. Thus, ROMs are usually equipped with numerical stabilization or closure models in order to account for the effect of the discarded modes. The literature on ROM closures and stabilizations is large and growing fast. In this paper, instead of reviewing all the ROM closures and stabilizations, we took a more modest step and focused on one particular type of ROM closure and stabilization that is inspired by large eddy simulation (LES), a classical strategy in computational fluid dynamics (CFD). These ROMs, which we call LES-ROMs, are extremely easy to implement, very efficient, and accurate. Indeed, LES-ROMs are modular and generally require minimal modifications to standard (“legacy”) ROM formulations. Furthermore, the computational overhead of these modifications is minimal. Finally, carefully tuned LES-ROMs can accurately capture the average physical quantities of interest in challenging convection-dominated flows in science and engineering applications. LES-ROMs are constructed by leveraging spatial filtering, which is the same principle used to build classical LES models. This ensures a modeling consistency between LES-ROMs and the approaches that generated the data used to train them. It also “bridges” two distinct research fields (LES and ROMs) that have been disconnected until now. This paper is a review of LES-ROMs, with a particular focus on the LES concepts and models that enable the construction of LES-inspired ROMs and the bridging of LES and reduced-order modeling. This paper starts with a description of a versatile LES strategy called evolve–filter–relax (EFR) that has been successfully used as a full-order method for both incompressible and compressible convection-dominated flows. We present evidence of this success. We then show how the EFR strategy, and spatial filtering in general, can be leveraged to construct LES-ROMs (e.g., EFR-ROM). Several applications of LES-ROMs to the numerical simulation of incompressible and compressible convection-dominated flows are presented. Finally, we draw conclusions and outline several research directions and open questions in LES-ROM development. While we do not claim this review to be comprehensive, we certainly hope it serves as a brief and friendly introduction to this exciting research area, which we believe has a lot of potential in the practical numerical simulation of convection-dominated flows in science, engineering, and medicine.

Multi-lump, resonant Y-shape soliton, complex multi kink solitons and the solitary wave solutions to the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation for incompressible fluid

The major contribution in this paper is to inquire into some new exact solutions to the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation (BLMPE) which plays a major role in area of the incompressible fluid. Taking advantage of the Cole-Hopf transform, we extract its bilinear form. Then two different kinds of the multi-lump solutions are probed by applying the new homoclinic approach. Secondly, the Y-shape soliton solutions are explored via assigning the resonance conditions to the N-soliton solutions. Additionally, the complex multi kink soliton solutions (CMKSSs) are investigated through the Hirota bilinear method. Lastly, some other wave solutions including the kink and anti-kink solitary wave solutions are developed with the aid of two efficacious approaches, namely the variational method and Kudryashov method. In the meantime, the profiles of the accomplished solutions are displayed graphically via Maple.

A robust three-dimensional numerical model for heat transfer characteristics in sintered–grooved thin flat heat pipes

In the current research, a robust three-dimensional numerical model is developed for thin flat heat pipes (TFHPs) with a hybrid sintered–grooved wick structure. Numerical simulations for laminar incompressible flow in liquid wick and ideal gas incompressible flow in the vapor core are performed to predict temperature, pressure, and velocity profiles. The model utilized non-Darcy transport through a porous wick to determine liquid flow in the liquid-wick section. The mass flow rate of the fluid at the liquid–vapor interface is modeled using kinetic theory. Furthermore, the hybrid wick structure is modeled as an inhomogeneous porous medium. Additionally, this formulation enhances the stability and convergence of the numerical solution and accelerates the solving time. The developed model is validated with experimental data, showing very good agreement with axial wall temperatures, with a maximum error of about 2% in steady-state conditions. The numerical results, including system pressure, wall temperature, mass transfer at the liquid and vapor interface, and velocity magnitude streamlines, are investigated for a comprehensive understanding of the flow physics and performance of the hybrid wick. The results show that, at heat inputs of 5, 10, 20, and 30 W, the thermal efficiency of hybrid wick TFHP is 4.9%, 10.4%, 34.38%, and 23.3%, respectively, greater than that of the grooved wick. The TFHP with a hybrid wick indicates the best thermal efficiency at a heat input of 20 W, with a thermal resistance of 0.95 K/W.

Simulation of the Effect of Hemolysis on Thrombosis in Blood-Contacting Medical Devices

Heart failure, broadly characterized by the gradual decline of the ability of the heart to maintain adequate blood flow throughout the body's vascular network of veins and arteries, is one of the leading causes of death worldwide. Mechanical Circulatory Support is one of the few available alternative interventions for late-stage heart failure with reduced ejection fraction. A ventricular assist device is surgically implanted and connected to the left and or right heart ventricles to provide additional bloodflow, off-loading the work required by the heart to maintain circulation. Modern mechanical circulatory support devices generate non-physiological flow conditions that can lead to the damage and rupture of blood cells (hemolysis), and the formation of blood clots (thrombosis), which pose severe health risks to the patient. It is essential to improve prediction tools for blood damage to reduce the risk of hemolysis and thrombosis. A simulation-based approach examines the interaction between hemolysis and thrombosis. Incompressible finite-volume computational fluid dynamics simulations are executed on an open-hub axial flow ventricular assist device. A continuum model of thrombosis and the intrinsic coagulation process is extended to include the effect of hemolysis. The model accounts for the effect of activation of platelets by shear stress, paracrine signaling, adhesion, and hemoglobin and ADP released during hemolysis. The effect of hemolysis with thrombosis is modelled by accounting for the hyper-adhesivity of von-Willebrand Factor on extracellular hemoglobin, and the increased rate of platelet activation induced by ADP release. Thrombosis is assessed at varying inflow rates and rotor speeds, and cases are executed where thrombosis is affected by ADP release and Hb-induced hyper-adhesivity. It is found that there is a non-negligible effect from hemolysis on thrombosis across a range of rotor speeds, and that hyperadhesivity plays a dominant role in thrombus formation in the presence of hemolysis.

Stability of plane parallel flow revisited for particle-fluid suspensions

Abstract An alternative model is proposed for hydrodynamic stability of plane parallel flow of an incompressible Newtonian fluids with suspended solid particles. For heavy particle-laden dusty gases with negligible particle volume fraction, the effective complex-form mean velocity in the modified Orr-Sommerfeld equation derived by the present model is showed to be essentially identical to the well-known Saffman's classical results. In the limit cases of small or large Stokes number of particles, simple formulas are derived for the effective Reynolds number ratio of the particle-laden suspension to the clear fluid without particles under otherwise identical conditions. The derived formula for particles of finite particle-to-fluid density ratio and small Stokes number is verified by comparing predicted results with known data, although a comparison of the derived formula with known results for particles of finite density ratio and large Stokes number cannot be made here due to the lack of available data. It is hoped that the present work could offer a conceptually novel and relatively simplified model for hydrodynamics of solid particle-fluid suspensions.

Impact of multiple slips and thermal radiation on heat and mass transfer in MHD Maxwell hybrid nanofluid flow over porous stretching sheet

This study investigates the two-dimensional magnetohydrodynamic (MHD) boundary-layer flow over a stretching sheet embedded in a porous medium, focusing on the innovative use of hybrid nanofluids. The research has practical applications in heat exchangers, nanofluid technology, porous media, and MHD systems. Key governing parameters, including internal heat sources/sinks, multiple slips, and thermal radiation, are analyzed for their impact on the flow. The nanofluid consists of hybridized nanoparticles (Alumina-Magnetite) dispersed in a water and ethylene glycol mixture (WEG-50:50). Assuming steady-state, incompressible, and laminar flow with small boundary layer thickness and constant nanofluid properties, the governing equations for continuity, momentum, energy, and species concentration are formulated. The fluid is modeled as a non-Newtonian (Maxwell) fluid. The resulting nonlinear ordinary differential equations system, with specified boundary conditions, is solved using the Runge-Kutta integration scheme implemented in MAPLE 23. Numerical results of heat transfer rates are validated against existing data, showing a 12 % increase in the Nusselt number for the WEG-Al2O3 nanofluid and a 20 % increase for the hybrid WEG- Al2O3–Fe3O4 nanofluid. It is demonstrated that skin friction decreases by up to 15 % with increased thermal Grashof number and that the Nusselt number can be reduced by up to 10 % due to magnetic effects. Overall, hybrid nanofluids generally demonstrate higher Nusselt and Sherwood numbers, enhancing heat transfer efficiency.

Fluidic Multichambered Actuator and Multiaxis Intrinsic Force Sensing.

Soft robots have morphological characteristics that make them preferred candidates, over their traditionally rigid counterparts, for executing physical interaction tasks with the environment. Therefore, equipping them with force sensing is essential for ensuring safety, enhancing their controllability, and adding autonomy. At the same time, it is necessary to preserve their inherent flexibility when integrating sensory units. Soft-fluidic actuators (SFAs) with hydraulic actuation address some of the challenges posed by the compressibility of pneumatic actuation while maintaining system compliance. This research further investigates the feasibility of utilizing the incompressible actuation fluid as the means of actuation and of multiaxial sensing. We have developed a hyperelastic model for the actuation pressure, acting as a baseline pressure. Any disparities from the baseline have been mapped to external forces, using the principle of pressure-based fluidic soft sensor. Computed tomography imaging has been used to examine inner deformation and validate the analytically derived actuation-pressure model. The induced stresses within the SFA are examined using COMSOL simulations, contributing to the development of a calibration algorithm, which accounts for geometric and cross-sectional nonlinearities and maps pressure variations with tip forces. Two force types (concentrated and distributed) acting on our SFA under different configurations are examined, using two experimental setups described as "Point Load" and "Distributed Force." The force sensing algorithm achieves high accuracy with a maximum absolute error of 0.32N for forces with a magnitude of up to 6N.

Celestial Choreography: Optimizing Mars Mission Trajectories through Gravity Assists

Mars exploration has become a focal point for medical, technological, and human endeavours. The success of these missions closely depends on optimizing spacecraft trajectories to ensure performance and cost-effectiveness. This paper delves into the significance of trajectory optimization and the pivotal role gravity assists play in interplanetary missions, particularly those aimed at Mars. In our study, we applied advanced simulation tools, including MATLAB, to model and optimize mission trajectories. Our research also includes Computational Fluid Dynamics (CFD) simulations of the Mars probe, focusing on incompressible flow tests around the probe's frame. A novel aspect of our design is the addition of a turbo-dynamic fan mounted on the outer boundary of the rover. This innovation is intended to reduce the descent velocity of the probe through the Martian atmosphere, improving landing precision and safety. Furthermore, our study explores the Olympus Mons area, a towering 27 km high Martian volcano, as a prime location for sample collection. By optimizing the trajectory and fuel usage, our simulations show how samples can be efficiently collected and returned to Mars orbit, ultimately facilitating their return to Earth. The trajectory calculations and visualizations provided offer valuable insights for future missions, aiming to balance fuel efficiency and mission success. This research not only highlights the quantitative benefits of trajectory optimization through gravity assists but also showcases the practical implications of innovative design improvements in space exploration. The lessons learned from our simulations and analyses are poised to significantly impact future Mars missions, paving the way for more efficient and effective exploration strategies.

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

Based on the Hirota bilinear method, we systematically investigate the (3+1)-dimensional Boiti-Leon-Manana-Pempinelli (BLMP) equation in incompressible fluids and main results include: (1) the formulas of N-kink-soliton solutions and the bound states of multi solitons are all presented, (2) the lump solution is derived by the positive quadratic function method, (3) the interactional solutions are given, i.e., one lump interacts with one- and two-kink-soliton, (4) some special periodic solutions are discussed, i.e., lump-periodic solutions and homoclinic breather solutions.

A new kind of Robe’s problem with charged bodies

This paper studies the motion of charged test particle, moving in the outermost layer of a heterogeneous body (taken as first primary) filled with incompressible homogeneous viscous fluid and second primary is taken as point mass, whereas both the primaries are assumed to be charged. We compute the equations of motion of test particle (the third body) and stationary points (circular, axial and out-of-plane stationary points). And also, the stability of stationary points is examined utilizing characteristics equations and Routh–Hurwitz criterion. In addition to this, the numerical analysis of stationary points and their stability are worked out for different values of parameters.

The quantum perfect fluid in 2D

We consider the field theory that defines a perfect incompressible 2D fluid. One distinctive property of this system is that the quadratic action for fluctuations around the ground state features neither mass nor gradient term. Quantum mechanically this poses a technical puzzle, as it implies the Hilbert space of fluctuations is not a Fock space and perturbation theory is useless. As we show, the proper treatment must instead use that the configuration space is the area preserving Lie group {S\mathrm{Diff}}SDiff. Quantum mechanics on Lie groups is basically a group theory problem, but a harder one in our case, since {S\mathrm{Diff}}SDiff is infinite dimensional. Focusing on a fluid on the 2-torus T^2T2, we could however exploit the well known result {S\mathrm{Diff}}(T^2)\sim SU(N)SDiff(T2)∼SU(N) for N\to ∞N→∞, reducing for finite NN to a tractable case. SU(N)SU(N) offers a UV-regulation, but physical quantities can be robustly defined in the continuum limit N\to∞N→∞. The main result of our study is the existence of ungapped localized excitations, the vortons, satisfying a dispersion \omega \propto k^2ω∝k2 and carrying a vorticity dipole. The vortons are also characterized by very distinctive derivative interactions whose structure is fixed by symmetry. Departing from the original incompressible fluid, we constructed a class of field theories where the vortons appear, right from the start, as the quanta of either bosonic or fermionic local fields.

Transient flow and heat transfer characteristics of single-phase nanofluid past a stretching sheet under the influence of thermal radiation and heat source

This work aims to investigate the unsteady hydromagnetic free convective flow of a viscous, electrically incompressible fluid influenced by an inclined magnetic field, radiation, and heat source. Specifically, it explores the behavior of water-based nanofluids under these conditions. The Newton-Raphson shooting technique combines the 4th-order Runge-Kutta approach to obtain dimensionless and accurate solutions to the governing equations. The study assesses flow characteristics and heat transfer properties over various parameter values. The outcomes are visualized through graphical representations of velocity, temperature, skin friction coefficient, and the local Nusselt number. The present study examines the impact of copper (Cu), silver (Ag), alumina (Al2O3), and titanium dioxide (TiO2) nanoparticles in water as the base fluid on the percentage increase in skin friction and Nusselt number under various physical conditions. Suction increases skin friction by 10–15 % and the Nusselt number by a similar margin, whereas injection can reduce these metrics. Radiation enhances heat transfer, resulting in a 5–10 % increase in skin friction and a 10–15 % rise in the Nusselt number, with nanoparticles like Ag showing the most substantial effects due to their superior thermal properties.

Simulations With Compressible Multiphase Formulation on Heat Transfer Studies in a Rocket Thrust Chamber With Experimental Validation

Abstract In the combustor for rocket engines, liquid film cooling is a widely adopted technique for restricting the structural components to the acceptable bounds for the successful operation of the propulsion systems. Multiple cooling techniques for thrust chamber walls are favored along with the coolant film in propulsion systems operating at higher chamber pressures by incorporating an ablative cooling mechanism for the nozzle. The adoption of combination will result in challenges in simulation studies due to the presence of multiphase phenomenon in the system. The current article presents the effects of these two cooling methods on a thrust chamber wall studied through compressible multiphase formulations. A majority of the previous studies have used incompressible flow equations to model coolant film behavior and associated heat transfer. The present study utilizes an approach utilizing compressible multiphase flow to simulate the behavior of the compressible hot gas flow and the incompressible coolant liquid film accounting for phase change effects, vapor diffusion into hot gas, radiation effects on coolant surface, liquid entrainment, and blowing effects due to vapor formation at interface. Film-cooling effects on ablative nozzle accounting for pyrolysis phenomenon due to material decomposition governed by Arrhenius expression are also emphasized. The outcome of the numerical model showed good agreement with available test data in literature, and results from the tests done in-house. The model described in the present study was able to support the actual evidence of liquid film cooling being able to preserve the walls of the thrust chamber from severe internal thermal environment and prevent ablation on surface of nozzle.

Thermal and flow characteristics in a square chamber with a nanoencapsulated phase-change material–water nanofluid under a linear temperature variation at all walls

In this study, the two-dimensional, steady-state, and incompressible flow and thermal behaviors of a water-based nanoencapsulated phase-change material (NE-PCM) nanofluid within a closed chamber were investigated, considering the impact of buoyancy. A novel approach was introduced by implementing linearly varying temperature conditions along all chamber walls. The effective dynamic viscosity and thermal conductivity correlations, derived experimentally, were used to model the governing equations. These equations were then rendered dimensionless through suitable transformations and solved using the Galerkin finite-element method. Results showed that the phase change region’s width increased with higher Rayleigh numbers, scaled phase change bonds, NE-PCM volume fractions, and fusion temperatures between 0.1 and 0.5, but decreased with fusion temperatures between 0.6 and 0.9. The highest Nusselt number occurred along the bottom wall for a fusion temperature range of 0.4–0.5. For optimal thermal performance, a square chamber with linearly varying temperature walls and a fusion temperature of 0.5 is recommended.

Analytical and Computational Modeling of Relaxation Times for Non-Newtonian Fluids

With the availability of efficient and sophisticated finite element analysis (FEA) and computational fluid dynamics (CFD) tools, engineering designs are becoming more software-driven and simulation-based. However, the insights relevant to engineering designs tend to be hidden within massive temporal and spatial data produced with full-fledged three-dimensional simulations. In this paper, we present a preliminary study of the controlled intermittent dispensing of a typical non-Newtonian glue employed in the manufacturing of electric vehicles (EVs). The focus of the study is on the scaling issues derived from different computational and analytical models of interest and importance to the precision control of this non-Newtonian fluid, the lowest dynamic viscosity of which at extremely high shear rates is nearly four million times that of water. More specifically, the abrupt change of the inlet pressure with a constant outlet or ambient pressure and various modeling strategies for transient viscous internal flow with both Newtonian and non-Newtonian fluids are modeled and compared. The analytical and computational results of the developing Newtonian fluid, i.e., water, are derived and computed for validation and verification purposes before the actual applications to the developing non-Newtonian fluid. The concept of a well-established relaxation time before the onset of the steady solution for Newtonian fluids has been validated with both analytical and computational approaches before its expansion and adoption to non-Newtonian fluids with complex rheological behaviors. Other issues attributed to transient operations and precision controls of non-Newtonian fluid delivery involve the pressure pulse and pressure wave propagation within the flexible pipe with compressible or almost incompressible non-Newtonian fluids with a constant pressure at the outlet and a constant mass flow rate or average axial velocity at the inlet, which will be addressed in a separate paper.

Investigation of vibration of nanorotating plates submerged in viscous-moving fluid medium

ABSTRACT In view of the great importance of dynamical behavior prediction of nanostructures in the fluid media and their various applications in biomedical engineering, aerospace, etc. in this research, the free vibration behavior of a nano-scale rotating plate coupled with an incompressible viscous fluid is studied. To this end, nonlocal elasticity theory is adopted to apply small-scale effects. Using the Navier–Stokes relation, the interaction forces between the fluid and nanorotating plate are obtained. In order to solve the governing differential equations, the Galerkin method is utilized, and the system’s vibration frequency response has been obtained for the clamped-free-free-free boundary condition.

Numerical Analysis of MHD Casson Fluid Flow over a Stretching Surface with Chemical Reaction and Variable Thermal Conductivity

The motivation of the current article is to explore the Numerical analysis of MHD Casson fluid flow over a Stretching surface. Three dimensional, non-linear of an incompressible fluid flow in the presence of chemical reaction and variable thermal conductivity is considered. The mathematical model effectively describes the current flow analysis. The Governing equations are simplified with the help of boundary layer approximations. Non-linear coupled equations for momentum, energy and mass transfer are tackled with MATLAB bvp4c. The behavior of various non-dimensional parameters which are involved in the derived set of equations are described and explained in detailed through graph.

Lagrangian Split-Step Method for Viscoelastic Flows.

This research addresses and resolves current challenges in meshless Lagrangian methods for simulating viscoelastic materials. A split-step scheme, or pressure Poisson reformulation of the Navier-Stokes equations, is introduced for incompressible viscoelastic flows in a Lagrangian context. The Lagrangian differencing dynamics (LDD) method, which is a thoroughly validated Lagrangian method for Newtonian and non-Newtonian incompressible flows, is extended to solve the introduced split-step scheme to simulate viscoelastic flows based on the Oldroyd-B constitutive model. To validate and evaluate the new method's capabilities, the following benchmarks were used: lid-driven cavity flow, droplet impact response, 4:1 planar sudden contraction, and die swelling. These findings highlight the LDD method's effectiveness in accurately simulating viscoelastic flows and capturing large deformations and memory effects. Even though the extra stress was directly modeled without any regularization approach, the method produced stable simulations for high Weissenberg numbers. The stability and performance of the the Lagrangian numerics for complex temporal evolution of material properties and stress responses encourage its use for industrial problems dealing with polymers.