Unsteady Motion Research Articles

Exploring the nanomechanical concepts of development through recent updates in magnetically guided system

This article outlines an analytical analysis of unsteady mixed bioconvection buoyancy-driven nanofluid thermodynamics and gyrotactic microorganisms motion in the stagnation domain of the impulsively rotating sphere with convective boundary conditions. To make the equations physically realistic, zero mass transfer boundary conditions have been used. The Brownian motion and thermophoresis effects are incorporated in the nanofluid model. Magnetic dipole effect has been implemented. A system of partial differential equations is used to represent thermodynamics and gyrotactic microorganisms motion, which is then transformed into dimensionless ordinary differential equations. The solution methodology is involved by homotopy analysis method. The results obtained are based on the effect of dimensionless parameters on the velocity, temperature, nanoparticles concentration and density of the motile microorganisms profiles. The primary velocity increases as the mixed convection and viscoelastic parameters are increased while it decreases as the buoyancy ratio, ferro-hydrodynamic interaction and rotation parameters are increased. The secondary velocity decreases as viscoelastic parameter increases while it increases as the rotation parameter increases. Temperature is reduced as the Prandtl number and thermophoresis parameter are increased. The nanoparticles concentration is increased as the Brownian motion parameter increases. The motile density of gyrotactic microorganisms increases as the bioconvection Rayleigh number, rotation parameter and thermal Biot number are increased.

UNSTEADY ROTATIONAL MOTION OF A MICROPOLAR FLUID INSIDE A RIGHT CIRCULAR CYLINDER USING STATE SPACE APPROACH

In this work, the unsteady rotational motion of an incompressible micropolar fluid inside a right circular cylinder is investigated. The classical no-slip and no-spin boundary conditions are proposed. The problem is solved analytically using the state space approach together with Laplace transform technique. The inverse Laplace transform is carried out numerically using a numerical technique based on Fourier series expansion. Numerical results for the flow field functions are represented graphically for different values of the time and micropolarity parameters.

Passive mechanical heat/mass exchange enhancement by semi-confined laminar parallel wall jets

Many different approaches have been investigated in the literature to achieve efficient heat and mass exchangers in applications in several fields such as mechanical, aeronautical or biomedical engineering. Some of these engineering devices need to efficiently mix two fluids at different temperature or concentrations, achieving a decent mixing at a low power cost, and using passive mechanical elements if possible. This paper introduces and analyses numerically the novel application of two parallel wall jets to enhance mixing by vortex shedding induced mechanically. The numerical approach is the non-uniform finite difference approximation, used for the first time in the study of mixing mechanics. The parallel wall jets are constrained within a channel, which can be a simple and passive easily manufactured machine with high potential as scalable laminar mixing device. Different wall jet geometries and Reynolds numbers have been tested with a verified&validated CFD code based on non-uniform finite difference approximation. This analysis allowed to predict configurations that lead to unsteady oscillatory motion. In general, it has been observed that for a range of laminar wall jets, a small channel ratio seems a very efficient option for heat/mass transfer, thanks to the intense oscillation generated in the flow downstream, which enhances mixing with low power requirement.

Development of supercritical motion and internal jumps within lock-release radial currents and draining flows

When released from rest in a cylindrical reservoir, relatively dense fluid flows radially and may drain freely over an edge or may propagate along the underlying boundary as a gravity current. Here we show that in both scenarios the unsteady fluid motions develop the same supercritical state, a phenomenon that does not occur in equivalent two-dimensional flows and which strongly influences the ensuing dynamics, even at long times after the release. In particular, we demonstrate the onset and persistence of supercritical outflow when fluid drains over an edge, and the development of internal bores within gravity current flow.

Application of time-domain methods for marine hydrodynamic and hydroelasticity analyses of floating systems

ABSTRACT The application of transient three-dimensional numerical code ITU-WAVE is presented for the prediction of hydrodynamic characteristics of floating bodies. The time histories of unsteady motions are directly presented with respect to Impulse Response Functions (IRFs). First-order steady forces of wave-resistance, sinkage force and trim moment are solved as the steady-state limit of surge radiation IRF. The numerical prediction of second-order mean force is presented using near-field method based on the direct pressure integration. The hydrodynamic and structural parts are fully coupled through modal analysis for the solution of hydroelastic analysis. A stiff structure is then studied assuming that contributions of rigid body modes are much bigger than elastic modes. A discrete control of latching is used to increase the bandwidth of the efficiency of Wave Energy Converters (WEC). ITU-WAVE numerical results for different floating bodies show satisfactory agreements compared to analytical, other numerical and experimental results.

Основы теории силового импульсного устройства

The article discusses a mathematical model of a power impulse device, which allows you to select the characteristics of the ejected liquid jet, such as the velocity at the moment of ejection, the pressure created in the nozzle of the power impulse device, etc., by changing the parameters of the device. A feature of the proposed mathematical model, which significantly distinguishes it from the previously considered models, is that the model was considered for the case of unsteady motion. This state of the medium in a power impulse device is the most characteristic, therefore the results obtained are more general. It is shown that, in contrast to the steady motion of a liquid, in the case of unsteady motion, an additional term appears, which can be defined as a head having an inertial character. It can be seen from the proposed mathematical model that the presence of an inertial head leads to the appearance of a flow deceleration effect, which, in turn, leads to an increase in the total liquid head in the direction of the flow. The pressure generated in the barrel acts against the direction of the hydraulic resistance. All of the above is applicable only for a certain moment in time or for the case when the acceleration of the fluid is constant. If the acceleration changes, then the action of the heads along the fluid flow is a function of time. This circumstance makes it possible to apply the result obtained with unsteady motion to create devices that form a high-pressure jet. A distinctive feature of the considered model is that it analyzes the behavior of the fluid in the power impulse device for two cases: 1. the volume of fluid in the barrel of the power impulse unit is greater than the volume of the nozzle; 2. the volume of fluid in the barrel is less than or equal to the volume of the nozzle. The results of the analysis showed that in the first case, the initial velocity of liquid ejection significantly exceeds this velocity in the second case. That is, it is the first case that is of practical importance.

Suppressing unsteady motion of shock wave by high-frequency plasma synthetic jet

Three Plasma Synthetic Jet Actuators (PSJA) under the high-frequency actuation are used to control the Shock Wave Boundary Layer Interaction (SWBLI), a high-speed schlieren image processing method based on spatial Fourier transform as well as snapshot proper orthogonal decomposition were used to study the control effect of high-frequency plasma synthetic jet on low-frequency unsteadiness of SWBLI. The analysis of the base flow shows that the separated shock wave actually has both large- and small-amplitude vibrations at low frequency. And the results revealed that the PSJA with an operating frequency of 2 kHz has the ability to reduce the energy of low-frequency component of shock wave motion, indicating that the 2 kHz actuation can effectively suppress low-frequency unsteadiness of the separated wave. Compared with the actuation frequency of 2 kHz, the energy of low-frequency component of the shock wave is enhanced under the 8 kHz actuation, which aggravates the low-frequency unsteady motion of the shock wave. It is likely that the actuation frequency is too high, thus the intensity of the precursor shock wave induced by PSJA becomes weaker. Additionally, as the 4 kHz actuation is applied, the pulsation of the separation region was enhanced, it is speculated that the actuation frequency is coupled with the oscillation frequency of the separation region.

Integral of the Euler Equations for 3D Motion of a Compressible Medium

We consider the classical Euler equations governing the 3D unsteady isothermal motion of an ideal compressible medium in the absence of external mass forces and barotropy, where the pressure, density, and velocity components are unknown. We propose a procedure for reducing the original problem to a family of simpler problems by introducing new associated unknowns.

Effects of pressure on propagation characteristics of methane-air edge flames within two-dimensional mixing layers: A numerical study

The effects of pressure on propagation of laminar edge flames were numerically investigated using an OpenFOAM-6 platform developed with multicomponent transport properties. With various equivalence ratio gradients (∇ϕ) as inlet conditions, propagation of non-stationary edge flames in two-dimensional mixing layers at three pressures (0.5 bar, 1.0 bar and 2.0 bar) were studied. The heat release rate increases with increasing pressure and decreases with increasing ∇ϕ due to flame curvature and stretch. The linearity between flame curvature K and ∇ϕ is revealed. The K and slope of this linearity are both larger under high pressure. Flame stretch is dominated by flow strain and flame curvature rather than unsteady flame motion. With increasing ∇ϕ and pressure, stretch rate κ shows increasing feature due to larger curvature and stronger flow strain. The obvious negative linear dependence of local flame speed Sd on κ is revealed under three pressures. The range of Karlovitz number under three pressures are 0.2~1.4, indicating that edge flames are weakly stretched and the linear correlation between Sd and κ could be explained by weakly stretched flame theory. Compared with positive dependence of mass diffusion term Sdd on K, the dominating negative dependence of reaction term Sdr on K leads to negative correlation of Sd with K. Global flame speed UF shows non-monotonic feature with increasing ∇ϕ under three pressures, which is mainly due to non-monotonic upstream velocity reduction Udrop. Flame stretch is important for the shift from critical gradient ∇ϕcd (for maximum Udrop) to smaller ∇ϕcF (for maximum UF) and stronger decreasing feature of UF thanUdrop under large ∇ϕ.

A review of turbulent skin-friction drag reduction by near-wall transverse forcing

The quest for reductions in fuel consumption and CO2 emissions in transport has been a powerful driving force for scientific research into methods that might underpin drag-reducing technologies for a variety of vehicular transport on roads, by rail, in the air, and on or in the water. In civil aviation, skin-friction drag accounts for around 50% of the total drag in cruise conditions, thus being a preferential target for research. With laminar conditions excluded, skin friction is intimately linked to the turbulence physics in the fluid layer closest to the skin. Hence, research into drag reduction has focused on methods to depress the turbulence activity near the surface. The most effective method of doing so is to exercise active control on the near-wall layer by subjecting the drag-producing flow in this layer to an unsteady and/or spatially varying cross-flow component, either by the action of transverse wall oscillations, by embedding rotating discs into the surface or by plasma-producing electrodes that accelerate the near-wall fluid in the transverse direction. In ideal conditions, drag-reduction margins of order of 50% can thereby be achieved. The present article provides a near-exhaustive review of research into the response of turbulent near-wall layers to the imposition of unsteady and wavy transverse motion. The review encompasses experiments, simulation, analysis and modelling, mainly in channel flows and boundary layers. It covers issues such as the drag-reduction margin in a variety of actuation scenarios and for a wide range of actuation parameters, the underlying physical phenomena that contribute to the interpretation of the origin of the drag reduction, the dependence of the drag reduction on the Reynolds number, passive control methods that are inspired by active control, and a forward look towards possible future research and practical realizations. The authors hope that this review, by far the most extensive of its kind for this subject, will be judged as a useful foundation for future research targeting friction-drag reduction.

Toward a fully resolved volume of fluid simulation of the phase inversion problem

This paper presents an enstrophy-resolved simulation of the phase inversion problem using the volume of fluid (VOF) method. This well-known benchmark for modeling multiphase flows features a buoyancy-driven unsteady motion of a light fluid into a heavy one followed by several large- and small-scale interfacial processes such as deformation, ligament formation, interface breakup, and coalescence. A fully resolved description of such flow is advantageous for a priori and a posteriori evaluations when developing new subgrid-scale closure models for large eddy simulation of two-phase flows. However, most of the previous attempts in performing the direct numerical simulation of this problem have been unsuccessful to reach grid-independent high-order flow statistics such as enstrophy. The key contribution of this paper lies in proposing a new converging configuration for this problem by reducing the Reynolds and Weber numbers. The new setup reaches grid convergence for all the flow characteristics on a 512^3 grid. Particularly, the enstrophy which has always revealed a grid-dependent behavior in all the previous studies converges for the proposed setup. Also, we analyze the temporal evolution of interfacial structures including the statistics of the total interfacial area during the process on different grid resolutions. First, no convergence on the interfacial area is observed and the possible reasons for lack of convergence are discussed. The potential remedies are investigated through a comprehensive parameter study. The findings highlight that (i) the enstrophy always converges for these moderate Re and We numbers, and (ii) the convergence of the total interfacial area is sensitive to the choice of initial and wall boundary conditions. Then, a new setup based on this sensitivity analysis is proposed that succeeded in full convergence for enstrophy and a partial convergence for the total interfacial area. The numerical simulations were carried out using the VOF solvers of OpenFOAM with a comparison between the algebraic and geometric schemes. Besides, the convergence of size distribution of dispersed structures is investigated. The present study provides insight into the possible directions toward a DNS of phase inversion problem with all the flow and interfacial structures resolved, which is essential for the future development of multiphase flow models.

Analytical Solutions for Two Mixed Initial-Boundary Value Problems Corresponding to Unsteady Motions of Maxwell Fluids through a Porous Plate Channel

Two unsteady motions of incompressible Maxwell fluids between infinite horizontal parallel plates embedded in a porous medium are analytically studied to get exact solutions using the finite Fourier cosine transform. The motion is induced by the lower plate that applies time-dependent shear stresses to the fluid. The solutions that have been obtained satisfy all imposed initial and boundary conditions. They can be easily reduced as limiting cases to known solutions for the incompressible Newtonian fluids. For a check of their correctness, the steady-state solutions are presented in different forms whose equivalence is graphically proved. The effects of physical parameters on the fluid motion are graphically emphasized and discussed. Required time to reach the steady-state is also determined. It is found that the steady-state is rather obtained for Newtonian fluids as compared with Maxwell fluids. Furthermore, the effect of the side walls on the fluid motion is more effective in the case of Newtonian fluids.

Axisymmetric Slow Motion of a Porous Spherical Particle in a Viscous Fluid Using Time Fractional Navier–Stokes Equation

In this paper, we present the unsteady translational motion of a porous spherical particle in an incompressible viscous fluid. In this case, the modified Navier–Stokes equation with fractional order time derivative is used for conservation of momentum external to the particle whereas modified Brinkman equation with fractional order time derivative is used internal to the particle to govern the fluid flow. Stress jump condition for the tangential stress along with continuity of normal stress and continuity of velocity vectors is used at the porous–liquid interface. The integral Laplace transform technique is employed to solve the governing equations in fluid and porous regions. Numerical inversion code in MATLAB is used to obtain the solution of the problem in the physical domain. Drag force experienced by the particle is obtained. The numerical results have been discussed with the aid of graphs for some specific flows, namely damping oscillation, sine oscillation and sudden motion. Our result shows a significant contribution of the jump coefficient and the fractional order parameter to the drag force.

Transient Large Eddy Simulation of Slurry Erosion in Submerged Impinging Jets

Abstract Submerged impingement jets are widely used in erosion/corrosion experiments as it is easy to control jet standoff distance, jet angle, and flow velocities in experiments. In addition to experiments, typically computational fluid dynamics (CFD) technique has been used to simulate slurry flow in this geometry to investigate erosion process and develop erosion models or equations. The traditional CFD simulations of erosion in this geometry use the Reynolds-averaged Navier–Stokes (RANS) equations with turbulence models. By using this technique, time-averaged fluid flow is revealed, and thus, time-averaged erosion rate can be obtained by tracking particles in the fluid flow field. However, this seemingly simple flow displays unsteady flow structures in the stagnation zone of the flow field and its effects on the erosion process were previously unclear. In this study, large eddy simulation (LES) is used to simulate unsteady fluid flow in different impingement jets in an Eulerian scheme. Then, transient particle tracking is performed in a Lagrangian scheme. Particles are injected randomly at the inlet plane and tracked to simulate unsteady erosion that occurs on the target surface. Finally, an erosion equation is used to calculate solid particle erosion rates. The LES Eulerian–Lagrangian erosion modeling is further validated by available experimental data for fluid velocities and an erosion profile. The results show that the accuracy of erosion prediction of small particles is improved significantly by using the LES method. In addition, the unsteady particle motion and erosion process can be revealed by using this method.

Large eddy simulation of a supersonic lifted jet flame in the high-enthalpy coflows

The stabilization mechanism of a supersonic lifted jet flame in the heated coflows should be attributed to the competition between autoignition and the propagation of active kernels at the flame base. As a result, the characteristics of the lifted hydrogen jet combustion gradually vary along the axial direction, which have not yet been deeply addressed in the previous studies. Highly-resolved large eddy simulation of a hydrogen jet injection into the air flow is carried out in this paper, the particular emphasis of which is placed on the evolution process of the turbulent structures as well as the flameholding mechanism. To analyze the effect of turbulence on the chemistry, an assumed probability density function method is adopted to close the source term of the governing equations. And the temporal and spatial resolution of the numerical schemes is high enough to capture the unsteady motion inside the supersonic reactive flowfeild. Predicted concentration of some important species agrees well with that measured by the experimental methods, demonstrating the responsibility of numerical results. From the instantaneous images, large eddy simulation reproduces the three-dimensional flowfield generated by the interaction of the inner jet and heated air flow. According to the time-averaged analysis, the combustion flowfield can be divided into three stages, namely the initial mixing, autoignition and subsequent turbulent flame. Evidently, the supersonic reactive flow passes through the transition from autoignition to the partially premixed flame, and the statistical features along the axial direction change correspondingly. Further, the effect of small-scale turbulent fluctuations on the reactive front within the shear layer is analyzed in detail, and the significant founding is propitious to understand the turbulent combustion regime in high-enthalpy conditions.

Propagation of one-dimensional planar and nonplanar shock waves in nonideal radiating gas

The present study seeks to investigate a quasilinear hyperbolic system of partial differential equations which describes the unsteady one-dimensional motion of a shock wave of arbitrary strength propagating through a nonideal radiating gas. We have derived an infinite hierarchy of the transport equation which is based on the kinematics of one-dimensional motion of shock front. By using the truncation approximation method, an infinite hierarchy of transport equations, which governs the shock strength and the induced discontinuities behind it, is derived to study the kinematics of the shock front. The first three transport equations (i.e., first, second, and third-orders) are used to study the growth and decay behavior of shocks in van der Waals radiating gas. The decay laws for weak shock waves in nonradiating gas are entirely recovered in the second-order truncation approximation. The results obtained by the first three approximations for shock waves of arbitrary strength are compared with the results predicted by the characteristic rule. Also, the effect of nonideal parameters and radiation on the evolutionary behavior of shock waves are discussed and depicted pictorially.

Low-frequency unsteadiness mechanisms in shock wave/turbulent boundary layer interactions over a backward-facing step

Abstract

Challenges and procedures for experiments with steady and unsteady model velocities in a water towing tank

Challenges for steady and unsteady model motion in a large water towing tank and procedures to overcome them are the focus of the presented work. Some challenges are attributed to experiments conducted in water, whereas others are uniquely ascribed to a towing tank facility. Data convergence and outlier detection are studied based on the phase averaged pressure in order to ensure proper data quality. Pressure measurements are performed with non-surface mounted sensors. Therefore, inertia effects are detrimental when the attached tubing is not fully de-aired. A procedure for de-airing the pressure sensor cavity and its tubing is described. An iterative approach is developed that compensates for nonlinear distortion of the model’s velocity profile. Further, vibration effects are examined by distinguishing mechanical and flow-induced frequencies that scale with the instantaneous model velocity. Sloshing waves are excited, which are a function of the water basin size. The first sloshing mode defines the required sensor offset time in between test cases when prevailing sloshing waves have not fully decayed. This appropriate selection of sensor offset time reduces data scatter and enables a reasonable waiting time in between test cases. A skim plate installed just below the water surface offers a potential solution to alleviate surface wave effects over the model.

On a hyperbolic system of equations in the problem of unsteady fluid motion

We consider a nonlinear system of the first-order partial differential equations with constant coefficients admitting a solution of the traveling wave type. Such systems are used in applied research to describe the dynamics of unsteady water movement in a pressure pipeline. In this paper, we propose methods for obtaining exact solutions in the case of an inhomogeneous equation of fluid motion under restrictions on the right-hand side in the form of a function. A special feature of the present research is reduction of the problem under study to the equations integrable in elementary functions.

Unsteady motion past a sphere translating steadily in wormlike micellar solutions: a numerical analysis

Abstract