Kinematic Viscosity Of Fluid Research Articles

Resolved CFD–DEM coupling simulation using Volume Penalisation method

A resolved CFD–DEM coupling model for the simulation of particulate flows is proposed in this work. The Volume Penalisation (VP) method, which is a family of the continuous forcing Immersed Boundary (IB) method, is employed to express the particle–fluid interaction. A smooth mask function is used to avoid sharp transition between the solid (particle) and fluid domains that may cause numerical oscillation with moving particles. Optimal permeability is employed to reduce the model error associated with the VP method. It is determined as a function of only the interface thickness and fluid kinematic viscosity. The proposed model is accurate, easy to implement with any discretisation scheme, and only requires small computational overhead for particle–fluid interaction. Several simulations are performed to test the validity of the proposed model in various systems, i.e. from dilute to relatively dense flows, and the results show good agreement with the exact solution or empirical correlation. It is found that the error can be scaled with the ratio between the gap and interface thickness. The proposed model is also applied to predict the relative viscosity of suspensions and the density segregation in fluidised beds.

Nonequilibrium Scaling of the Turbulent-Nonturbulent Interface Speed in Planar Jets.

The length scale which, combined with the fluid's kinematic viscosity ν, defines the local average speed of the turbulent-nonturbulent interface has been postulated to be the smallest (Kolmogorov) length scale η of the turbulence Corrsin and Kistler, [NACA Report No.1244, 1955, p.1033.]. This is indeed the case when the turbulence dissipation rate obeys the Kolmogorov equilibrium cascade scaling, but in the presence of the nonequilibrium turbulence dissipation scaling the average local turbulent-nonturbulent interface speed scales as ν/λ, instead of ν/η, where λ is the Taylor length. We derive this theoretically and confirm it experimentally in the range of distances between 20 and 50 nozzle widths of a turbulent planar jet.

Asymptotic scaling of drag in flat-plate turbulent boundary layers

A new asymptotic −1/2 power-law scaling is derived from the momentum integral equation for the drag in flat-plate turbulent boundary layers. In the limit of infinite Reynolds number, the appropriate velocity scale for drag is found to be M/ν, where M is the boundary layer kinematic momentum rate and ν is the fluid kinematic viscosity. Data covering a wide range of Reynolds numbers remarkably collapse to a universal drag curve in the new variables. Two models, discrete and continuous, are proposed for this universal drag curve, and a robust drag estimation method, based on these models, is also presented.

Steady flow in a rapidly rotating spheroid with weak precession: I

The celebrated Poincaré (1910) steady solution, the uniform vorticity flow in a precessing spheroid, which is realized in the inviscid interior region outside the boundary layer in the strong spin and weak precession limit, is derived, as a unique solution analytically without any prior assumption on the spatial structure, and its singular behavior for a sphere is resolved. Assuming that the spin and precession axes are respectively parallel and perpendicular to the symmetry axis of the spheroid, we denote the spin and precession angular velocities by and respectively, and define the Reynolds number Re = and the Poincaré number , where a is the equatorial radius and ν is the kinematic viscosity of fluid. An ellipsoidal coordinate system is introduced, which makes it possible to express the solution explicitly in a separable form. It is shown that only the uniform vorticity flow can develop as a steady flow in the inviscid limit. The vorticity, relative to the spinning spheroid, is in magnitude and points to or against the z-axis for an oblate (c < 1) or a prolate (c > 1) spheroid. This expression of vorticity magnitude diverges to infinity for a sphere (c = 1), where the inviscid solution is degenerate. This apparent singular behavior of the vorticity is resolved by introducing viscosity and analyzing the flow by invoking the torque balance equation for a spheroid close to a sphere in the limit , where . It is found that the vorticity vector changes the orientation smoothly by 180° over and that the parallel and the perpendicular (to the spin axis) components of vorticity is expressed, up to the nontrivial leading order, as the twice of −0.7876Po2/[(2.620δ)2 + (0.2585δ + 1 − c)2] and , respectively. The latter is included in Busse ()'s formula, whereas the former is new. An analysis of the same flow as the present paper from a different approach was performed recently by Zhang et al (). Unfortunately, however, an inconsistency is found in their results.

Numerical Study of Highly Viscous Fluid Sloshing in the Real-Scale Membrane-Type Tank

The highly viscous liquid (glycerin) sloshing is investigated numerically in this study. The full-scale membrane-type tank is considered. The numerical investigation is performed by applying a two-phase numerical model based on the spatially averaged Navier-Stokes equations. Firstly, the numerical model is validated against the available numerical model and a self-conducted experiment then is applied to systematically investigate the full-scale sloshing. In this study, two filling levels (50% and 70% of the tank height) are considered. The fluid kinematic viscosity is fixed at a value being 6.0 × 10−5 m2/s with comparative value to that of the crude oil. A wide range of forcing periods varying from 8.0 s to 12.0 s are used to identify the response process of pressures as well as free surface displacements. The pressures are analyzed along with breaking free surface snapshots and corresponding pressure distributions. The slamming effects are also demonstrated. Finally, the frequency response is further identified by the fast Fourier transformation technology.

Formation and decay of eddy currents generated by crossed surface waves

The mass-transport induced by crossed surface waves consists of the Stokes and Euler contributions which are very different in nature. The first contribution is a generalization of Stokes drift for a plane wave in ideal fluid and the second contribution arises due to the fluid viscosity and it is excited by a force applied in the viscous sublayer near the fluid surface. We study the formation and decay of the induced mass-transport theoretically and experimentally and demonstrate that both contributions have different time scales for typical experimental conditions. The evolution of the Euler contribution is described by a diffusion equation, where the fluid kinematic viscosity plays the role of the diffusion coefficient, while the Stokes contribution evolves faster, feeling the additional damping near the system boundaries. The difference becomes more pronounced if the fluid surface is contaminated. We model the effect of contamination by a thin insoluble liquid film presented on the fluid surface with the compression modulus being the only non-zero rheological parameter of the film. Then the Euler contribution into the mass-transport becomes parametrically larger and the evolution of the Stokes contribution becomes parametrically faster. The parameter is the same in both cases and it is equal to the quality factor of surfaces waves, which is modified by the presence of a surface film. We infer the value of the compression modulus of the film by fitting the results of transient measurements of eddy currents and demonstrate that the obtained value leads to the correct ratio of amplitudes of horizontal and vertical velocities of the wave motion and is in reasonable agreement with the measured dissipation rate of surface waves.

Calculation of the Optimum Cone Angle of a Confuser Used for Reversive-Jet Cleaning of Metal Surfaces against Corrosion

The modern industrial production of the Republic of Belarus is characterized by the absence of its own raw material base and significant dependence on imported energy carriers and material resources supplied at world prices. When working in such conditions, production efficiency can be achieved through all-round economy and creation of modern energyand resource-saving technologies. However implementation of such technologies, for example, laser cutting and welding, cladding, flame spraying, painting, etc. directly depends on quality of cleaning metal surfaces from corrosion. Theoretical and experimental studies conducted at the Department of Shipbuilding and Hydraulics of the Belarusian National Technical University have shown that it is very economical to remove corrosion products from metal surfaces using new technology of reverse jet cleaning. The reverse jet cleaning technology is based on a physical principle which presupposes that a jet of working fluid (pulp based on river sand or bentonite clay) rotates 180º when it hits the surface to be cleaned and it leads to an increase in jet impact on the surface to be cleaned by 1.5–2 times due to occurrence of a reactive component. In order to ensure a marked jet reversal an original case design has been developed which is characterized by a patent novelty. One of the main elements in this design is a confuser-shaped stream-forming device. Theoretical investigations on pressure losses of working fluid in a confuser channel which are based on the study of functional at the extremum have made it possible to obtain a dependence for calculation of an optimal cone angle at a turbulent mode of motion within the range of Reynolds numbers 4000 &lt; Re &lt; 3 ×106 while taking into account an influence of working fluid density, its dynamic or kinematic viscosity, average velocity movement of working fluid, confuser radii.

An experimental investigation of flow-induced vibration of high-side-ratio rectangular cylinders

This study reports an experimental investigation on the flow-induced vibration (FIV) of elastically mounted rectangular cylinders with high-side-ratio in free-stream flow. The side ratio (σ), defined as the ratio of the cross-flow side width (h) to the streamwise side width (b) of the cylinder, namely σ=h∕b, was varied from 2.0 to 5.0. The fluid–structure system was modelled using a low-friction air-bearing system in conjunction with a free-surface water channel facility. The structural vibration was characterised over the reduced velocity range of 2⩽U∗=U∕(fnwh)⩽16, where U is the free stream velocity and fnw is the natural frequency of the system in quiescent water. The corresponding Reynolds number varied in the range of 940⩽Re=Uh∕ν⩽8200, where ν is the fluid kinematic viscosity. The mass ratio, defined as the ratio of the oscillating mass to the displaced fluid mass, varied from 6.56 to 12.18, depending on the cylinder models. It was found that the vibration response was dominated by vortex-induced vibration (VIV) response for U∗≲8.4 for all the σ cases tested. In the VIV lock-in regime, the local peak amplitude response was found to increase with σ (i.e. from A∕h≃1.05 for σ=2.0 to A∕h≃1.69 for σ=5.0). Interestingly, beyond the VIV lock-in regime, while a galloping response was observed for the cases of σ⩽4.0, where the vibration amplitude increased linearly with U∗, the σ=5.0 case exhibited a bounded galloping regime with the amplitude increasing up to A∕h≃1.44 at U∗=10.8, prior to an abrupt drop to A∕h≈0.35 of a desynchronisation regime for higher U∗ values. The results suggest that this unexpected collapse of galloping response could be due to exceeding the relative incidence angle threshold for possible galloping.

Fundamentals of Differential Particle Inertial Focusing in Symmetric Sinusoidal Microchannels

Focusing and separation of particles such as cells at high throughput is extremely attractive for biomedical applications. Particle manipulation based on inertial effects requires a high flow speed and thus is well-suited to high-throughput applications. Recently, inertial focusing and separation using curvilinear microchannels has been attracting a great amount of interest because of the linear structure for parallelization, small device footprint, superior particle-focusing performance, and easy implementation of particle separation. However, the curvature directions of these microchannels alternate, leading to variations in both the magnitude and direction of the induced secondary flow. Accumulation of this variation along the channel causes unpredictable behaviors of particles. This paper systematically investigates the inertial-focusing phenomenon in low-aspect-ratio symmetric sinusoidal channels. First, we comprehensively studied the effects of parameters such as viscosity, flow conditions, particle size, and geometric dimensions of the microchannel on differential particle focusing. We found that particle inertial focusing is generally independent of fluid kinematic viscosity but highly dependent on particle size, flow conditions, and channel dimensions. Next, we derived an explicit scaling factor and included all four dimensionless parameters (particle-blockage ratio, curvature ratio, Dean number, and channel aspect ratio) in a single operational map to illustrate the particle-focusing patterns. Finally, we proposed a rational guideline to intuitively instruct the design of channel dimensions for separation of a given particle mixture.

The drag coefficient and settling velocity of natural sediment particles

This article reports a study in which drag coefficient is defined more comprehensively. The coefficient is defined as a function of particle nominal diameter, gravitational acceleration, the ambient fluid kinematic viscosity, and the particle shape. This new definition is different from the conventional definitions proposed in the literature based on direct equations as a function of particle Reynolds number. The conventional definitions appear to be a simplification of drag coefficient and thus decreasing the accuracy of the estimations. Instead, the proposed equation in this article indicates that on average the drag coefficient estimation can be improved at least 3.77% compared to the proposed drag coefficient widely used in the literature. The improved drag coefficient was used to derive a more accurate settling velocity equation in which the effect of particle shape is directly incorporated in the settling velocity equation. Both equations were validated using well known datasets and accurate experiments from the literature as well as new experiments conducted for this purpose in the current research. The experiments cover a wide range of particle shape and a variety of specific gravity. The outcomes of the current study contribute to the use of settling velocity in river hydraulic applications proposing a simpler but more accurate procedure.

The onset of transient turbulence in minimal plane Couette flow

The onset of transient turbulence in minimal plane Couette flow has been identified theoretically as homoclinic tangency with respect to a simple edge state for the Navier–Stokes equation, i.e., the gentle periodic orbit (the lower branch of a saddle-node pair) found by Kawahara &amp; Kida (J. Fluid Mech., vol. 449, 2001, pp. 291–300). The first tangency of a pair of distinct homoclinic orbits to this periodic edge state has been discovered at Reynolds number $Re\equiv Uh/\unicode[STIX]{x1D708}=Re_{T}\approx 240.88$ ($U$, $h$, and $\unicode[STIX]{x1D708}$ being half the difference of the two wall velocities, half the wall separation, and the kinematic viscosity of fluid, respectively). At $Re&gt;Re_{T}$ a Smale horseshoe appears on the Poincaré section through transversal homoclinic points to generate a transient chaos that eventually relaminarises. In numerical experiments a sustaining chaos, which is a consequence of period-doubling cascade stemming from the upper branch of another saddle-node pair of periodic orbits, is observed in a narrow range of the Reynolds number, $Re\approx 240.40$–240.46. At the upper edge of this $Re$ range it is found that the chaotic set touches the lower branch of this pair, i.e., another edge state. The corresponding chaotic attractor is replaced by a chaotic saddle at $Re\approx 240.46$, and subsequently this saddle touches the gentle periodic edge state on the boundary of the laminar basin at the tangency Reynolds number $Re=Re_{T}$. After this crisis on the boundary of the laminar basin, for $Re&gt;Re_{T}$, chaotic transients that eventually relaminarise can be observed.

The Investigation of Mutual Interference Vortex Flow around Two Circular Cylinders by Flow Visualization and Pressure Measurement

In order to understand the aspect of the mutual interference flow from two circular cylinders, the visual observation experiment and the pressure measurement experiment were performed by use a water flow apparatus. Two circular cylinders with a diameter of D=10mm were used, and they have been arranged at staggered or tandem. The flow velocity was U=0.25m/s (Re=UD/í, í is kinematic viscosity of fluid). The dye oozing streak method was used in the visualization experiment. In the pressure measurement experiment, the pressure on the surface of a circular cylinder was detected by the single tube manometer, and measurement was performed by image processing using a computer. As a result, distribution of the circular cylinder surface pressure coefficient CP corresponding to the flow pattern and it in each circular cylinder arrangement was obtained. The drag coefficient CD was calculated from the pressure coefficient CP, and change of the resistance in each arrangement was found.

Turbulence statistics in smooth wall oscillatory boundary layer flow

Turbulence characteristics of an asymmetric oscillatory boundary layer flow are analysed through two-component laser-Doppler measurements carried out in a large oscillatory flow tunnel and direct numerical simulation (DNS). Five different Reynolds numbers, $R_{\unicode[STIX]{x1D6FF}}$, in the range 846–2057 have been investigated experimentally, where $R_{\unicode[STIX]{x1D6FF}}=\tilde{u} _{0max}\unicode[STIX]{x1D6FF}/\unicode[STIX]{x1D708}$ with $\tilde{u} _{0max}$ the maximum oscillatory velocity in the irrotational region, $\unicode[STIX]{x1D6FF}$ the Stokes length and $\unicode[STIX]{x1D708}$ the fluid kinematic viscosity. DNS has been carried out for the lowest three $R_{\unicode[STIX]{x1D6FF}}$ equal to 846, 1155 and 1475. Both experimental and numerical results show that the flow statistics increase during accelerating phases of the flow and especially at times of transition to turbulent flow. Once turbulence is fully developed, the near-wall statistics remain almost constant until the late half-cycle, with values close to those reported for steady wall-bounded flows. The higher-order statistics reach large values within a normalized wall distance of approximately $y/\unicode[STIX]{x1D6FF}=0.2$ at phases corresponding to the onset of low-speed streak breaking, because of the intermittency of the velocity fluctuations at these times. In particular, the flatness of the streamwise velocity fluctuations reaches values of the order of ten, while the flatness of the wall-normal velocity fluctuations reaches values of several hundreds. Far from the wall, at locations where the vertical gradient of the streamwise velocity is zero, the skewness is approximately zero and the flatness is approximately equal to 3, representative of a normal distribution. At lower elevations the distribution of the fluctuations deviate substantially from a normal distribution, but are found to be well described by other standard theoretical probability distributions.

Annular swirling liquid layer with a hollow core

A thick turbulent annular liquid layer that swirls inside a fixed pipe is studied by means of surface observations and stereoscopic particle image velocimetry in an index-matched nozzle facility. This flow combines the complexities of swirling and free-surface turbulence. The free surface of the layer changes the boundary condition compared to filled swirling pipes and introduces the equivalent of a hollow core. The liquid layer shares similarities with turbulent open-channel flows, with the high centrifugal force across the layer having a similar effect to that of gravity in channel flows. At the surface, the restoring forces are surface tension and centrifugal acceleration. The particular nozzle under study has been envisioned for inertial confinement fusion, but the flow has relevance to systems such as compact separators or liquid rocket fuel injectors. Data are acquired at five downstream locations from the nozzle exit for four Reynolds numbers for subcritical flows. Injection flow rate and fluid kinematic viscosity are controlled independently, which allows adjusting independently the Reynolds and Taylor–Reynolds numbers. This also enables control of the centrifugal force at the free surface to test the effects of turbulence intensity on the free surface in regimes where air entrainment and droplet ejection occur. The swirl number is fixed by the design of the nozzle. From velocimetry data, mean velocity and turbulence statistics are extracted. For all the conditions tested, three flow regimes are identified: developing, developed, and transitional. The developed regime appears self-similar on the mean; the swirl creates a favourable pressure gradient that sustains the axial flow and confines the boundary layer near the wall. Large coherent vortex structures are identified in the layer. A simple model is proposed to describe the layer thickness and the velocity distribution in it. In the transitional regime, helical varicose waves generated by centrifugal instability are observed on the surface. Additionally, wall effects are visible in the bulk of the flow, and the main flow features are large overturning motions.

The Renormalization-Group Method in the Problem on Calculation of the Spectral Energy Density of Fluid Turbulence

In order to find the shape of energy spectrum within the framework of the model of stationary homogeneous isotropic turbulence, the renormalization-group equations, which reflect the Markovian nature of the mechanism of energy transfer along the wavenumber spectrum, are used in addition to the dimensional considerations and the energy balance equation. For the spectrum, the formula depends on three parameters, namely, the wavenumber, which determines the upper boundary of the range of the turbulent energy production, the spectral flux through this boundary, and the fluid kinematic viscosity.

Mechanism of fluid production from the nanopores of shale

Fluid production from the nanopores of shale is elucidated by an analytical solution of the linearized compressible Navier-Stokes equations with no-slip condition for the pore-scale drainage flow from a small capillary in a matrix block to the surrounding fractures. The pore-scale drainage flow is driven by the volumetric expansion of the compressed fluid and it is always unsteady. It is shown that fluid is produced by the decay of a standing acoustic wave and the no-slip flow has a period-averaged mass flow rate (drainage rate) proportional to the square of the capillary radius which is two orders of magnitude higher than that from the Poiseuille's law. The drainage speed is found proportional to fluid's kinematic viscosity but independent of the capillary radius, allowing the fluid to escape to the fracture with a finite speed regardless how small the capillary is. This result represents a fundamental departure from the classical Poiseuille flow theory and it provides a unified mechanism on how shale fluid is produced.

Semi-Empirical Estimation of Dean Flow Velocity in Curved Microchannels

Curved and spiral microfluidic channels are widely used in particle and cell sorting applications. However, the average Dean velocity of secondary vortices which is an important design parameter in these devices cannot be estimated precisely with the current knowledge in the field. In this paper, we used co-flows of dyed liquids in curved microchannels with different radii of curvatures and monitored the lateral displacement of fluids using optical microscopy. A quantitative Switching Index parameter was then introduced to calculate the average Dean velocity in these channels. Additionally, we developed a validated numerical model to expand our investigations to elucidating the effects of channel hydraulic diameter, width, and height as well as fluid kinematic viscosity on Dean velocity. Accordingly, a non-dimensional comprehensive correlation was developed based on our numerical model and validated against experimental results. The proposed correlation can be used extensively for the design of curved microchannels for manipulation of fluids, particles, and biological substances in spiral microfluidic devices.

Energy spectrum of turbulent velocity pulsations in a wide range of wave numbers (renorm-group approach)

Abstract Based on the concept of cascade mechanism of energy transfer over the wave-number spectrum and related to the locality property of intermodal interactions forming the energy spectrum, the unified formula for spectral energy density is obtained that is valid in a wide range of wave numbers including both inertial and dissipation ranges. The form of the spectrum is governed by three parameters, namely, a value of wave number chosen as the normalization point assigned to the edge of the domain of the stochasticity emergence due to the development of instability of large-scale flows and the turbulent energy production, the spectral energy flux through the boundary of energy production domain in the wave-number space (the energy pumping rate), and the fluid kinematic viscosity.

A coin vibrational motor swimming at low Reynolds number

Low-cost coin vibrational motors, used in haptic feedback, exhibit rotational internal motion inside a rigid case. Because the motor case motion exhibits rotational symmetry, when placed into a fluid such as glycerin, the motor does not swim even though its vibrations induce steady streaming in the fluid. However, a piece of rubber foam stuck to the curved case and giving the motor neutral buoyancy also breaks the rotational symmetry allowing it to swim. We measured a 1 cm diameter coin vibrational motor swimming in glycerin at a speed of a body length in 3 seconds or at 3 mm/s. The swim speed puts the vibrational motor in a low Reynolds number regime similar to bacterial motility, but because of the vibration it is not analogous to biological organisms. Rather the swimming vibrational motor may inspire small inexpensive robotic swimmers that are robust as they contain no external moving parts. A time dependent Stokes equation planar sheet model suggests that the swim speed depends on a steady streaming velocity $V_{stream} \sim Re_s^{1/2} U_0$ where $U_0$ is the velocity of surface vibrations, and streaming Reynolds number $Re_s = U_0^2/(\omega \nu)$ for angular vibrational frequency $\omega$ and fluid kinematic viscosity $\nu$.

Impinging rotational stagnation-point flows

A rotational stagnation-point flow of fluid density ρ1 and kinematic viscosity ν1 impinges normal to another rotational stagnation-point flow of fluid density ρ2 and viscosity ν2. Results are compared with a previous study on the normal impingement of two Homann stagnation-point flows for which the flow in the far field is irrotational.