Nonslip Walls Research Articles

Artificial swim by undulating rigid flagellum with joint controllers

In this paper, we investigate the locomotion of artificial (robotic) swimmers by an undulating rigid flagellum, whose joints are controlled by actuators. The locomotion of a swimmer with an undulating rigid flagellum inside a two-dimensional channel sandwiched by two non-slip walls is numerically analyzed using the immersed boundary lattice Boltzmann method. Multi-relaxation-time scheme is applied to calculate the flow field under a high Reynolds number (Re). Our numerical results show that the optimal Re exists to maximize the locomotion distance, whereas the direction of locomotion can be reversed in the lower and higher Re limits.

Dynamics of flame extinction in narrow channels with cold walls: Heat loss vs acceleration

Propagation of a premixed flame from a closed to an open end in micro-channels with smooth non-slip isothermal walls is considered in the context of flame extinction dynamics. Powerful exponential flame acceleration in micro-channels with adiabatic walls has been demonstrated at the initial quasi-isobaric stage of the process [Bychkov et al., Phys. Rev. E 72, 046307 (2005)]. In contrast to the previous studies, here we investigate flame propagation in channels with isothermal walls. The problem is solved by means of high-fidelity laminar numerical simulations of the complete set of the Navier–Stokes combustion equations. For most of the problem parameter sets chosen, we obtain initial flame acceleration after ignition at the closed channel end. This acceleration resembles qualitatively the adiabatic case, but it develops noticeably slower, in an approximately linear regime instead of the exponential one and persists only for a limited time interval. Subsequently, heat loss to the walls reduces the temperature and hence the volume of the burnt gas behind the flame front, which produces a reverse flow in the direction of the closed channel end. When the amount of the burnt gas becomes sufficiently large, the reverse flow stops the acceleration process and drives the flame backwards with modifications of the flame front shape from convex to concave. Eventually, the flame extinguishes. Qualitatively, the process obtained reproduces a possible combustion failure during deflagration-to-detonation transition observed in previous experiments. We investigate the key characteristics of initial flame acceleration such as the acceleration rate and the maximum speed of the flame tip.

Computational Study of Premixed Flame Propagation in Micro-Channels with Nonslip Walls: Effect of Wall Temperature

This investigation evaluates the propagation of premixed flames in narrow channels with isothermal walls. The study is based on the numerical solution of the set of fully-compressible, reacting flow equations that includes viscosity, diffusion, thermal conduction and Arrhenius chemical kinetics. Specifically, channels and pipes with one extreme open and one extreme closed are considered such that a flame is sparked at the closed extreme and propagates towards the open one. The isothermal channel walls are kept at multiple constant temperatures in the range from Tw=300 K to 1200 K. The impact of these isothermal walls on the flame dynamics is studied for multiple radii of the channel (R) and for various thermal expansion ratios (Θ), which approximate the thermal behavior of different fuel mixtures in the system. The flame dynamics in isothermal channels is also compared to that with adiabatic walls, which were previously found to produce exponential flame acceleration at the initial stage of the burning process. The results show that the heat losses at the walls prevent strong acceleration and lead to much slower flame propagation in isothermal channels as compared to adiabatic ones. Four distinctive regimes of premixed burning in isothermal channels have been identified in the Θ−Tw−R space: (i) flame extinction; (ii) linear flame acceleration; (iii) steady or near-steady flame propagation; and (iv) flame oscillations. The physical processes in each of these regimes are discussed, and the corresponding regime diagrams are presented.

Impacts of fuel nonequidiffusivity on premixed flame propagation in channels with open ends

The present study scrutinizes premixed flame dynamics in micro-channels, thereby shedding light on advanced miniature micro-combustion technologies. While equidiffusive burning (when the Lewis number Le = 1) is a conventional approach adopted in numerous theoretical studies, real premixed flames are typically non-equidiffusive (Le ≠ 1), which leads to intriguing effects, such as diffusional-thermal instability. An equidiffusive computational study [V. Akkerman et al., Combust. Flame 145, 675–687 (2006)] reported regular oscillations of premixed flames spreading in channels having nonslip walls and open extremes. Here, this investigation is extended to non-equidiffusive combustion in order to systematically study the impact of the Lewis number on the flame in this geometry. The analysis is performed by means of computational simulations of the reacting flow equations with fully-compressible hydrodynamics and one-step Arrhenius chemical kinetics in channels with adiabatic and isothermal walls. In the adiabatic channels, which are the main case of study, it is found that the flames oscillate at low Lewis numbers, with the oscillation frequency decreasing with Le, while for the Le > 1 flames, a tendency to steady flame propagation is observed. The oscillation parameters also depend on the thermal expansion ratio and the channel width, although the impacts are rather quantitative than qualitative. The analysis is subsequently extended to the isothermal channels. It is shown that the role of heat losses to the walls is important and may potentially dominate over that of the Lewis number. At the same time, the impact of Le on burning in the isothermal channels is qualitatively weaker than that in the adiabatic channels.

Effects of Isothermal Wall Boundary Conditions on Rotating Detonation Engine

ABSTRACT Three-dimensional numerical simulations of rotating detonation engines (RDEs) are reported with stoichiometric hydrogen/air mixtures using Navier-Stokes equations with non-slip walls. The effects of isothermal wall boundary conditions at 300 K, 600 K and 900 K are investigated and further compared with the simulation under adiabatic walls. With isothermal walls of 300 K, axial detonation is formed, which further leads to the quenching of detonation. With 600 K isothermal walls, the detonation wave has a similar stably propagating process as adiabatic walls. However, due to the wall heat loss, a lower detonation velocity is obtained in the simulation with isothermal walls. With 900 K isothermal walls, it is found that detonation quenches at first due to the high temperature of the walls, then re-initiates as a result of the collisions of shock waves. In addition, the temperature and heat flux distributions in the outer wall are analyzed. Both the peak temperature and heat flux are found to appear at the detonation wavefront. The averaged heat flux in the detonation region is about three times of the averaged heat flux evaluated in the outer wall. Moreover, the averaged temperature and heat flux remain nearly unchanged in the post-detonation region. Our results are in agreement with experimental studies and provide some insights for RDE thermal management.

Aeroacoustic Characteristics of a Synchronized Fluidic Oscillator

A new opposite facing oscillator pair is presented where shared feedback channels enable synchronized sweeping of the exiting jets. The design has no moving parts and the oscillator pair is composed in a back-to-back configuration. The synchronized operation generates a near-field acoustic tonality and the objective is to determine the emitted directivity. The acoustic generation mechanisms were determined using compressible large eddy simulations, which was validated with hot-wire and microphone measurements. Different Reynolds number (Re) conditions up to 21,250 were analyzed for a synchronized oscillation with Strouhal number (St) of order 0.01. Dominant acoustic sources emerging during synchronized sweep oscillation were classified by the interpretation of directivity patterns for a selected flow rate. The near-field directivity pattern could be decomposed as a periodic signal consisting of one acoustic mode with a dipole-like pattern, showing two major lobes associated with the jet sweeping oscillation frequency: one acoustic monopole-like directivity for the first overtone; and dipole-like directivity with two lobes for the second harmonic. It is shown that the acoustic sources are generated by the synchronized pressure oscillation of the exiting jets. The vortical structures inside the fluidic oscillator interact with the non-slip walls. These manipulate the curvature of the central jet and causes an unsteady loading towards the discharge. The new fluidic oscillator design gives synchronized exiting sweeping jets and a large flow length scale near-field directivity pattern. These features give feedback type fluidic oscillators a wider application range.

Simulation of Combustion Flowfield in Porous Media with Lattice Boltzmann Method

In this paper, two-dimensional numerical modeling of a premixed porous combustion is presented by a Lattice Boltzmann approach. In this solution, the flow distribution is replaced by a pressure distribution equation using the Darcy and Forchheimer model as the multiple-relaxation-time code. The laminar propane-air mixture with Reynolds number of 100 and Prandtl number of 0.75 is put through a silicon carbide porous medium channel. The boundary conditions are included as the uniform inlet temperature and velocity, atmospheric output pressure, periodic wall temperature, and nonslip walls with initial zero gradient for products and reactants. For validation of this model, the presented data of temperature, molar concentration, and velocity comprised published data where the existence of acceptable agreements confirms the accuracy of this solution. The results show that, in the porous medium, the flame position is located at closer distance from the entrance of channel rather than the nonporous medium. Furthermore, the maximum temperature is reduced up to 5.8% when Darcy number is decreasing from 0.1 to 0.001, and with the reduction of Darcy number, the size of vortices is decreased. Moreover, when the porosity coefficient decreases, the size of high-temperature region decreases, and with increasing equivalence ratio from 0.6 to 1, the maximum temperature is significantly augmented with a value of 24.3%.

Numerical Simulation of Oxy-Fuel Premixed Combustion in a Supercritical CO2-diluted Environment.

Development of advanced supercritical carbon dioxide (sCO2) combustors for next-generation gas turbines requires deeper understanding of the dynamics and structure of CO2-diluted flames at supercritical conditions. To address this question, the key parameters of premixed supercritical oxy-methane combustion, such as the velocity, temperature and thickness of the flame front are scrutinized in the present work. The analysis is performed by means of the computational simulation of the combustion equations with fully-compressible hydrodynamics, transport properties (heat conduction, diffusion and viscosity) and one-step Arrhenius chemical kinetics. In addition, the real-gas thermodynamics and molecular properties are incorporated into the reacting-flow Navier-Stokes solver along with the Peng-Robinson equation of state. It is shown that an increase in a CO2-dilution rate makes the flame front thicker and reduces the unstretched laminar flame speed, as compared to that of non-diluted oxy-combustion. Starting with the planar flames, attained by means of the slip boundary conditions at the computational domain, the analysis is subsequently extended to the corrugated flames, produced by non-slip walls of the computational domain. While a corrugated flame front generally propagates faster than the planar one of similar thermal-chemical characteristics, the corrugated flame velocity not only diminishes with the dilution rate, but it also depends on the size/geometry of the combustor.

Three-dimensional simulation of a self-propelled fish-like body swimming in a channel

ABSTRACTIn this study, a three-dimensional simulation of a fish-like body swimming in a channel with non-slip walls was carried out to investigate the effects of kinematics on swimming performance. Self-propelled swimming in an inertial coordinate system was examined by using the direct forcing immersed boundary method. The fish body consisted of several rigid bodies and behaved analogously to a multi-segment robotic fish. The computational program was first validated by simulating fluid flow around a circular cylinder at Reynolds number (Re) =100 and Re = 1000, as well as around a settling particle. The results were compared with experimental and numerical results from past research in the area. A virtual parametric study of the tail-beat frequency, phase difference between neighboring body segments, and body amplitude was then conducted. The effect of the lateral and vertical distance between the model body and walls on swimming performance is also discussed. The results for the velocity and vorticity fields around the model body provided evidence for the mechanism of thrust generation and highlighted the effects of kinematics on swimming performance.

Dynamics and Morphology of Premixed Flame Propagation in Channels: Effects of the Lewis Number and Thermal Boundary Conditions

Equidiffusive combustion is a model, which is widely employed in analytical and computational studies, including those on premixed flame acceleration. However, realistic combustible mixtures are oftentimes far from the stoichiometry, being thereby strongly non-equidiffusive and thus requiring extra analyses. The present work addresses this demand by means of the computational simulations of the basic fully-compressible hydrodynamic and combustion equations. Specifically, here we focus on the non-equidiffusive flames at various thermal boundary conditions, including adiabatic or isothermal walls of the channels. A detailed parametric study is performed, with the key parameters of the problem being the Lewis number, Le, taken in the range 0.2 ≤ Le ≤ 2.0, the thermal expansion factor Θ, being 5 ≤ Θ ≤ 8, and the flame propagation Reynolds number, Re = R/PrLf, where Lf is the thermal flame thickness and Pr the Prandtl number. We used Re in the range 5 ≤ Re ≤ 30. It is shown that while Θ ~ 8 flames tend to accelerate exponentially in channel with adiabatic, nonslip walls; acceleration moderates to a linear trend for Θ ~ 5. Moreover, with the isothermal walls, acceleration moderates (with hot walls) or even terminates (with cold walls). Furthermore, it is found that a non-unity Le influences the flame dynamics notably in both adiabatic and isothermal channels. Namely, Le < 1 flames get extra strong corrugation and thereby spread much faster than equidiffusive ones. In contrast, Le > 1 flames are thickened and propagate slower.

Effect of Mechanistic Surface Conditions on Extremely Fast Flame Acceleration in Obstructed Cylindrical Pipes

Abstract: The Bychkov model of extremely fast flame acceleration in obstructed cylindrical pipes [Combust. Flame 157 (2010) 2012] employs a number of simplifying assumptions, including those of slip and adiabatic surfaces of the obstacles and the pipe wall. In the present work, the influence of various mechanistic surface conditions on the combustion process in cylindrical pipes with in-built parallel, tightly-spaced obstacles is scrutinized by means of the computational simulations of the axisymmetric combustion equations with fully-compressible hydrodynamics and Arrhenius chemical kinetics. Specifically, nonslip and slip surfaces are compared for the obstacles blockage ratio α in the range 1/3 ≤ α ≤ 2/3 and the spacing between the obstacles Δz in the range 0.25 ≤ Δz/R ≤ 2.0. It is shown that the impact of surface friction on flame acceleration is minor, 1.3~3.5%, being positive in a pipe with Δz/R = 0.5 and negative for Δz/R = 0.25. With the fact that the real boundary conditions are neither slip nor nonslip; but in between these categories, the present study thereby justifies the Bychkov model and makes its wider applicable to the practical reality. While this result can be naively anticipated and elucidated by the very fact that the flame dynamics is mainly driven by burning in the unobstructed portion of an obstructed pipe (i.e. far from the wall), the situation is, however, qualitatively different from that in the unobstructed pipes, where the flame dynamics in the events of slip and non-slip walls differ drastically (quantitatively) and conceptually (qualitatively).

A Lattice Boltzmann model for simulating water flow at pore scale in unsaturated soils

The Lattice Boltzmann (LB) method is an established prominent model for simulating water flow at pore scale in saturated porous media. However, its application in unsaturated soil is less satisfactory because of the difficulties associated with most two-phase LB models in simulating immiscible fluids, such as water and air, which have contrasting densities and viscosities. While progress has been made in developing LB models for fluids with high density ratio, they are still prone to numerical instability and cannot accurately describe the interfacial friction on water–air interface in unsaturated media. Considering that one important application of the LB model in porous materials is to calculate their hydraulic properties when flow is at steady state, we develop a simple LB model to simulate steady water flow at pore scale in unsaturated soils. The method consists of two steps. The first one is to determine water distribution within the soil structure using a morphological model; once the water distribution is known, its interfaces with air are fixed. The second step is to use a single-phase LB model to simulate water flow by treating the water–air interfaces as free-flow boundaries where the shear resistance of air to water flow is assumed to be negligible. We propose a method to solve such free-flow boundaries, and validate the model against analytical solutions of flows of water film over non-slip walls in both two and three dimensions. We then apply the model to calculate water retention and hydraulic properties of a medium acquired using X-ray computed tomography at resolution of 6 μm. The model is quasi-static, similar to the porous network model, but is an improvement as it directly simulates water flow in the pore geometries acquired by tomography without making any further simplifications.

Effect of thermal expansion on flame propagation in channels with nonslip walls

Propagation of premixed flames in narrow channels is investigated by means of extensive numerical simulations of a complete system of combustion and hydrodynamic equations, incorporating transport properties (thermal conduction, diffusion and viscosity) and Arrhenius chemical kinetics. The system includes mass conservation and Navier–Stokes equations as well as those for the energy and species balance. A flame propagates from the closed end of a channel to the open one. An initially planar flame front gets corrugated due to wall friction and thereby accelerates. It is shown that a flame exhibits an exponential state of acceleration only when the thermal expansion coefficient Θ exceeds a certain critical value Θ>Θc. The quantity Θc is tabulated as a function of the Reynolds number related to the flame propagation, Re, being Θc≈6 for Re=5∼20. The major flame characteristics such as the flame propagation speed and acceleration rate are scrutinized. It is demonstrated that the acceleration promotes with Θ but weakens with Re. In this respect, the present computational results support the theoretical prediction of Bychkov et al. Physical Review E 72 (2005) 046307 in a wide range of Θ and Re. While very good quantitative and qualitative agreement between numerical and theoretical results is found for realistically large thermal expansion, Θ⩾8, agreement deteriorates with decreasing Θ. Specifically, while the theory and modeling do not quantitatively agree for Θc<Θ<8, they nevertheless demonstrate a qualitative resemblance (the exponential state of acceleration). Finally, no exponential acceleration at Θ<Θc denotes that the theory completely breaks in that case, but this fits other works in the field and thereby allows reconciling various formulations on the flame acceleration.

Flame–sound interaction in tubes with nonslip walls

Flame interaction with sound is studied for a premixed flame propagating to the closed end of a tube with nonslip walls. The flow geometry is similar to that in the classical Searby experiments on flame–acoustic interaction [Combust. Sci. Technol. 81 (1992) 221]. The problem is solved by direct numerical simulations of the combustion equations. The flame–sound interaction strongly influences oscillations of the flame front. Particularly, sound noticeably increases the oscillation amplitude in comparison with that in an open tube with nonreflecting boundary conditions at the ends studied previously. Oscillations become especially strong in the second part of the tube, where flame pulsations are in resonance with the acoustic wave. Parameters of the flame oscillations are investigated for different values of the tube width and length. It is demonstrated that the oscillations are stronger in wider tubes, though the investigated tube width is limited by the computational facilities. In sufficiently wide tubes, violent folding of a flame front is observed because of the flame–acoustic resonance. By increasing the Lewis number, one also increases the oscillation amplitude.

Numerical simulation of Marangoni flow in partially confined half-zone liquid bridge of low-Prandtl-number fluids

Direct numerical simulation using a finite difference method was done to reveal the fundamental characteristics of the flow in a half-zone liquid bridge of low Prandtl number fluids with the free surface partially confined by oxide films (non-slip adiabatic rigid walls). The critical Marangoni number Ma c1 was calculated for several geometries, which are determined by the free surface ratio ( ξ= L w/ L, L w: length of the free surface, L: height of the whole liquid bridge) and the axial position of the free surface. When the oxide film exists between the free surface and the cold disc, the flow separates from the oxide film, and a weak cell with a counter flow arises near the cold disc. An axisymmetric flow exhibits a direct transition to an oscillatory flow, when the free surface ratio ξ is sufficiently small and free surface was located away from the cold disc.

Numerical bifurcation study of electrohydrodynamic convection in nematic liquid crystals.

We present the results of a numerical investigation of the Ericksen-Leslie equations for the problem of electrohydrodynamic convection in a nematic liquid crystal. The combination of a finite element approach and numerical bifurcation techniques allows us to provide details of the basic flow and include the physically relevant effect of nonslip side walls. We are also able to include material properties as parameters and this permits us to draw comparisons with available experimental data. We then compare and contrast the bifurcation structure with that of Rayleigh-Bénard and Taylor-Couette flows and explore the role of symmetries by including a fringing electric field.

Time-dependent patterns in atomistically simulated convection.

Periodically varying roll patterns have been produced in molecular-dynamics simulation of two-dimensional Rayleigh-B\'enard convection using a hard-disk fluid in a square container with nonslip walls. In order to achieve the sufficiently high Rayleigh numbers required for clearly resolved time-dependent behavior the calculations involved systems containing almost 6\ifmmode\times\else\texttimes\fi{}${10}^{4}$ particles, an order of magnitude greater than the number needed to observe stationary convection patterns.

Vortices interacting with nonslip walls: Stirring and mixing of primary and secondary vorticity

The interaction of vortices with fixed boundaries is an important problem in many areas of practical interest. During the approach of the vortices to the wall, vorticity is created at the wall, and then mixing and stirring of primary and secondary vorticity lead to different scenarios that depend on the Re number. This problem is relevant to bursting in turbulent boundary layers, which is responsible for turbulence production. In the near-wall region of turbulent flows, vortex stretching plays a fundamental role. As a prelude to attempting the solution by direct simulation of 3-D Navier–Stokes equations, it is convenient to describe the mechanism associated with 2-D or axisymmetric flows. In the present study, axisymmetric vortex rings and vortex dipoles approaching a nonslip flat wall have been considered. In both cases, experimental results based on flow visualization are available.1,2 The purpose of the present paper is to do a numerical simulation with the same conditions used in the real experiments and follow the flow evolution for a much longer time than has been possible in such experiments. Both for axisymmetric and 2-D cases the numerical simulation shows, as revealed by the experiments, that, at the initial stage, very thin layers of vorticity of sign opposite to that of the primary vortex are generated at the wall. This mechanism is almost independent of Re. This thin and intense layer immediately becomes unstable and rolls up creating a secondary vortex. This vortex interacts with the primary vortex and different flow structures are generated, depending on Re. The location where these structures form depends, in large measure, on whether vortex stretching is present or not. Particularly relevant to the bursting phenomenon is the case at intermediate Re (e.g., Re=1600). Here, a new dipole is created near the wall after multiple rebounding and pairing of secondary vortices. This new structure has sufficient strength to move itself away from the wall. We conclude that mixing and stirring of vorticity are the relevant mechanisms influencing the whole process in a two-dimensional simulation. This ejection of a new structure was previously noticed in the interaction of vortex rings with a wall. From flow visualization, Walker et al., at Re=Γ/ν&amp;gt;3500, observed the occurrence of azimuthal instabilities and, immediately after that, they noticed a new vortex ring was rapidly ejected away from the wall.2 From these observations, those authors argued that the ejection was due to the azimuthal instabilities. In the present paper, axisymmetric calculations have been done in the same range of numbers used in the experiment of Walker et al.2 From the time evolution of the vorticity distribution, we argue that vortex pairing is the main mechanism that contributes to the generation of the new ring rather than azimuthal instabilities. The numerical simulations clearly show that this new ring is created above the primary ring and not at its interior.

Vortex dipole rebound from a wall

Accurate numerical simulations of vortex dipoles impinging on flat boundaries have revealed interesting new features. In the case of free-slip boundaries the dipole does not rebound from the wall. In the case of nonslip walls rebounding occurs and complex interactions of secondary and tertiary vortices appear. The numerical simulation of the first dipole rebound from the wall agrees with experimental visualizations. Numerical experiments extending in time beyond the real experiments show multiple rebounding. Each rebound is associated with the detachment of a secondary vorticity layer from the wall, these layers merge, and at a value of Reynolds number Re=1600, form a new dipole. This dipole has sufficient circulation to induce on itself a motion in the opposite direction to the motion of the initial dipole.

Linear growth rates for the Rayleigh-Bénard instability in cylindrical geometry

We report theoretical growth rates for the Rayleigh–Bénard instability when the fluid layer is contained by non-slip walls in a cylindrical geometry with diameter D and height L. Our results are for the growth rates of the first two axisymmetric modes as functions of the Prandtl number P and the aspect ratio γ≡D/2L. We have considered the two extreme cases of ideally insulating and ideally conducting side walls, and found that the growth rate is relatively insensitive to the choice of the thermal boundary conditions on the side walls. Our results are useful in understanding recent experimental measurements of the convective time-scale.