Zero-mean Velocity Research Articles

Experimental study of butanol droplet evaporation in a turbulent, high-pressure environment

An experimental investigation is conducted to study the vaporization behavior of butanol droplets in a turbulent environment at elevated pressure. A single droplet of butanol, with a diameter of 500 µm, is suspended at the intersection point of two micro-fibers positioned in the center of a fan-stirred spherical chamber. The latter is equipped with eight axial fans to generate an isotropic and homogeneous turbulent flow field with nearly zero-mean velocity. In this experiment, turbulence intensity and ambient pressure were varied from 0 to 1.5 m/s and from 1 to 10 bar, respectively, while ambient temperature was kept at room conditions. The experimental findings revealed that the butanol droplet squared diameter exhibited a linear relationship with time for the majority of the droplet lifetime. This observation suggests that the d2-law is applicable across all the test conditions explored in this study. Results showed that the vaporization rate of a butanol droplet decreases with ambient pressure and increases with turbulence intensity. The vaporization rate of butanol falls between that of heptane and decane, with closer proximity to decane. Furthermore, the comparison of these fuels indicates that the influence of turbulence on the vaporization rate is more significant for fuels with lower vapor mass diffusivity. Finally, published correlations based on Damköhler and Reynolds numbers are verified and found to hold for the butanol droplet vaporization data.

Anomalous statistics of particle spreading in quenched random velocity field

We study the motion of a random walker in two dimensional randomly oriented Manhattan lattice where each horizontal and vertical link in a regular square lattice is assigned a random direction. This model describes the anomalous diffusion properties of the tracer particles that are driven by a random unidirectional zero mean velocity field. By means of numerical analysis and with the use of qth order moment 〈xq(t)〉∼tqβ, we find the anomalous scaling exponent β=2∕3 that perfectly agrees with previous studies. We develop some precise results to understand the anomalous nature of random motion in random environments. This is done by the study of non-Gaussian properties of the probability density function, logarithmic scaling of the diffusion entropy and weak ergodicity analysis. It is also found that the mean exit times from a bounded domain is related to the fractal nature of the process.

Floating tracer clustering in divergent random flows modulated by an unsteady mesoscale ocean field

ABSTRACT Clustering of tracers floating on the ocean surface and evolving due to combined velocity fields consisting of a deterministic mesoscale component and a kinematic random component is analysed. The random component represents the influence of submesoscale motions. A theory of exponential clustering in random velocity fields is applied to characterise the obtained clustering scenarios in both steady and unsteady time-dependent mesoscale flows, as simulated by a comprehensive realistic, eddy-resolving, general circulation model for the Japan/East Sea. The mesoscale flow field abounds in transient eddy-like patterns modulating and branching the main currents, and the underlying time-mean flow component features closed recirculation zones that can entrap the tracer. The submesoscale flow component is modelled kinematically, as a divergent random velocity field with a prescribed correlation radius and variance. The combined flow induces tracer clustering, that is, the exponential growth of tracer density in patches with vanishing areas. The statistical topography methodology, which provides integral characteristics to quantify the emerging clusters, uncovers drastic dependence of the clustering rates on whether the mesoscale flow component is taken to be steady or time-dependent. The former situation favours robust exponential clustering, similar to the theoretically understood case of purely divergent and zero-mean random velocity. The latter situation, on the contrary, hinders exponential clustering due to significant advection of the tracer out of the nearly enclosed eddies, at the rate faster than the clustering rate.

Engineering passive swimmers by shaking liquids

The locomotion and design of microswimmers are topical issues of current fundamental and applied research. In addition to numerous living and artificial active microswimmers, a passive microswimmer was identified only recently: a soft, Λ-shaped, non-buoyant particle propagates in a shaken liquid of zero-mean velocity (Jo et al 2016 Phys. Rev. E 94 063116). We show that this novel passive locomotion mechanism works for realistic non-buoyant, asymmetric Janus microcapsules as well. According to our analytical approximation, this locomotion requires a symmetry breaking caused by different Stokes drags of soft particles during the two half periods of the oscillatory liquid motion. It is the intrinsic anisotropy of Janus capsules and Λ-shaped particles that break this symmetry for sinusoidal liquid motion. Further, we show that this passive locomotion mechanism also works for the wider class of symmetric soft particles, e.g. capsules, by breaking the symmetry via an appropriate liquid shaking. The swimming direction can be uniquely selected by a suitable choice of the liquid motion. Numerical studies, including lattice Boltzmann simulations, also show that this locomotion can outweigh gravity, i.e. non-buoyant particles may be either elevated in shaken liquids or concentrated at the bottom of a container. This novel propulsion mechanism is relevant to many applications, including the sorting of soft particles like healthy and malignant (cancer) cells, which serves medical purposes, or the use of non-buoyant soft particles as directed microswimmers.

Numerical study on mixed convection from a constant wall temperature circular cylinder in zero-mean velocity oscillating cooling flows

Fluid flow and heat transfer of mixed convection from a constant wall temperature circular cylinder in zero-mean velocity oscillating cooling flows have been simulated based on the projection method with two dimensional exponential stretched staggered cylindrical meshes. Cycle mean temperature and secondary streaming are obtained by the method of partial sums of the Fourier series. Present numerical results are validated by comparing the heat transfer results of free convection and the secondary streaming of pure oscillating flow over a circular cylinder to published experimental and numerical results. The complete structures of the cycle mean temperature and secondary streaming patterns are provided by numerical simulations over wide ranges of the Reynolds number, the Keulegan–Carpenter number and the Richardson number. Based on turning points of the curves of the overall Nusselt numbers versus Reynolds numbers and the characteristics of the cycle averaged temperature and flow patterns, the heat transfer can be divided into three linear regimes (conduction, laminar convection, and turbulent convection dominated regimes) and two non-linear transition regimes. The effects of wave directions, amplitudes, frequencies, and buoyancy forces on the enhancement of heat transfer are also investigated. The effective ranges of the governing parameters for heat transfer enhancement are identified.

Oscillatory Streaming Flow Based Mini/Microheat Pipe Technology

The sustained drive for faster and smaller micro-electronic devices has led to a considerable increase in power density. The ability to effectively pump and enhance heat transfer in mini-/microchannels is of immense technological importance. Using oscillatory flow to enhance the convective heat transfer coefficients in micro-/minichannels is one of many new concepts and methodologies that have been proposed. In this paper, a novel and simple concept is presented on oscillating streaming flow based mini/microheat pipe or heat spreader technology. Phenomena of the flow streaming can be found in zero-mean velocity oscillating flows in many channel geometries. Although there is no net mass flow (zero-mean velocity) passing through the channel, discrepancy in the velocity profiles between the forward and backward flows causes fluid particles near the walls to drift toward one end while particles near the centerline drift to the other end. This unique characteristic of flow streaming could be used for various applications. Some of the advantages include enhanced heat/mass transfer, pumpless fluid propulsion, multichannel fluid distribution, easy system integration, and cost-effective operation. Preliminary work has been conducted on scaling analysis, computer simulations, and visualization experiments of fluid streaming, propulsion, and multichannel distribution by flow oscillation in minitapered channels and channel networks. Results show that streaming flow has the potential to be used as a cost-effective and reliable heat pipe and/or as a heat spreader technique when fluid thermal conductivity is low.

Fluid Streaming in Micro/Minibifurcating Networks

In this study, we investigate the phenomena of flow streaming in micro-/minichannel networks of symmetrical bifurcations using computer simulations with analytical validation. The phenomena of the flow streaming can be found in zero-mean velocity oscillating flows in a wide range of channel geometries. Although there is no net mass flow (zero-mean velocity) passing through the channels, the discrepancy in velocity profiles between the forward flow and backward flow causes fluid particles near the walls to drift toward one end while particles near the centerline to drift toward the opposite end. The unique characteristics of flow streaming could be used for various applications. The advantages include enhanced mixing, pumpless fluid propulsion, multichannel fluid distribution, easy system integration, and cost-effective operation. The results of computer simulations showed that oscillation amplitude is the dominant effect on streaming velocity in channel networks. Streaming velocity was directly proportional to the oscillation frequency and can be used as a cost-effective and reliable convective transport means when the particle diffusivity is less than the fluid kinematic viscosity. A considerable amount of work is needed to further study and understand the flow streaming phenomenon.

Dissipation rate estimation from PIV in zero-mean isotropic turbulence

Measuring the turbulent kinetic energy dissipation rate in an enclosed turbulence chamber that produces zero-mean flow is an experimental challenge. Traditional single-point dissipation rate measurement techniques are not applicable to flows with zero-mean velocity. Particle image velocimetry (PIV) affords calculation of the spatial derivative as well as the use of multi-point statistics to determine the dissipation rate. However, there is no consensus in the literature as to the best method to obtain dissipation rates from PIV measurements in such flows. We apply PIV in an enclosed zero-mean turbulent flow chamber and investigate five methods for dissipation rate estimation. We examine the influence of the PIV interrogation cell size on the performance of different dissipation rate estimation methods and evaluate correction factors that account for errors related to measurement uncertainty, finite spatial resolution, and low Reynolds number effects. We find the Re λ corrected, second-order, longitudinal velocity structure function method to be the most robust method to estimate the dissipation rate in our zero-mean, gaseous flow system.

Measurement of pseudoturbulence intensity in monodispersed bubbly liquids for 10<Re<500

Experiments were performed to measure the velocities of both phases in a monodispersed bubbly flow in a vertical column. Using water and water-glycerin mixtures, measurements were obtained for a range of Reynolds numbers from 10 to 500. For all cases, the Weber number was below 2. To generate a uniform stream of bubbles, an array of identical capillaries was used. To avoid coalescence, a small amount of salt was added to the interstitial fluid, which did not affect the fluid properties significantly. Measurements of the bubble phase velocity were obtained using a dual impedance probe and through high-speed digital video processing. A measurement of the vertical component of the fluctuating liquid velocity was obtained using a flying hotwire technique, which resolved the deficiency of this technique for flows with zero-mean velocity. To the best of our knowledge, this technique has not been used to study bubbly liquids in the past. It was found that for all cases, the bubble velocity decreases as the mean gas volume fraction increases. For vanishing gas volume fraction, the mean bubble velocity was found to be smaller than that calculated for an isolated bubble. The flow agitation, characterized by the velocity variance both in the liquid and the bubble phases, increases with bubble concentration. The bubble velocity variance was found to rapidly increase with gas volume fraction but to reach a nearly constant value for concentrations higher than 1.5% for all cases. The liquid velocity variance was found to increase linearly with gas concentration for large Re; for low Re the increase was at a smaller rate. The variance, normalized with the mean bubble velocity squared, increased as the Reynolds number decreased. Direct comparisons are performed with recent theoretical and computational studies for the same range of conditions.

Asymmetric motion of a two-dimensional symmetric flapping model

A two-dimensional symmetric flapping model is studied in terms of the bifurcation using discrete vortex method. This model consists of two wings attached together at a hinge, and the flapping motion of the wings is symmetric with respect to the horizontal line. The center of mass of this model can move according to the hydrodynamic force generated by an interaction of the wing and vortices separated from boundary layer. The bifurcation parameter is a time scale of the dissipation, which is simplified to contrast the transition of the type of the motion. Bifurcation diagram shows that steady motion of zero-mean velocity (with symmetric flapping) is unstable in a parameter region, and that there is another region where two types of a steady stable flapping motion coexist. We illustrate these types of the motion.

Laminar convective heat transfer from a circular cylinder exposed to a low frequency zero-mean velocity oscillating flow

Heat transfer characteristics of a circular cylinder exposed to a slowly oscillating flow with zero-mean velocity were investigated. The flow oscillation amplitude and frequency were changed in the range where the flow remains laminar and fluid particle travels back and forth over much larger distance compared to the cylinder diameter. The time- and space-averaged Nusselt number was measured by transient method, while two-dimensional numerical simulation was conducted to discuss the instantaneous flow and thermal fields around the cylinder. It was found that the time- and space-averaged Nusselt number can be correlated with the oscillating Reynolds number and Richardson number. Unique heat transfer characteristics under oscillating flow condition can be seen at the phases when the cross-sectional mean velocity is small or increasing from small value. During such period, heat transfer can be enhanced due to the local fluid motion induced by the vortices around the cylinder, which once moved away but returned back by the reversed flow. This heat transfer enhancement, however, is countered by the local warming effect of the hot vortices clinging around the cylinder at such phases.

Evolution of turbulence in an oscillatory flow in a smooth-walled channel: a viscous secondary instability mechanism.

In this paper, a comparison is made of the evolution of turbulence in oscillatory channel flows with a zero-mean velocity in two and three dimensions, using the numerical technique of the lattice Boltzmann method. The results confirm a primary two-dimensional instability. Evidence is shown of a secondary, viscous three-dimensional instability mechanism acting in the oscillatory boundary layer, which is consistent with experimental observations.

A new correlation for turbulent mass transfer from liquid droplets

This paper presents a new correlation for mass transfer from single liquid droplets into a turbulent environment. Experiments were carried out under ambient room temperature and pressure. Homogeneous isotropic turbulence with zero-mean velocity was generated by eight identical electrical fans placed on the eight corners of a cubic chamber. The LDV technique was used to characterize the turbulence inside the chamber. The vaporization of fiber suspended droplets of five different n-alkanes and the bi-component droplet of n-heptane and n-decane mixtures subjected to varying turbulent kinetic energy is investigated by imaging techniques. For mono-component droplets the d 2-law holds for all fuels and turbulent kinetic energies, and the vaporization rates increase with increasing the turbulent kinetic energy. Bi-component droplets exhibit a sequential vaporization behavior for all mixtures and turbulent kinetic energies. The instantaneous vaporization rates increase with increasing turbulence kinetic energy and increasing volume fraction of the highest volatility component. The proposed correlation predicts the vaporization rates of mono and bi-component n-alkane droplets subjected to isotropic turbulence with zero-mean velocity.

Survival probability in a random velocity field

The time dependence of the survival probability, S(t), is determined for diffusing particles in two dimensions which are also driven by a random unidirectional zero-mean velocity field, v_x(y). For a semi-infinite system with unbounded y and x>0, and with particle absorption at x=0, a qualitative argument is presented which indicates that S(t)~t^{-1/4}. This prediction is supported by numerical simulations. A heuristic argument is also given which suggests that the longitudinal probability distribution of the surviving particles has the scaling form P(x,t)~ t^{-1}u^{1/3}g(u). Here the scaling variable u is proportional to x/t^{3/4}, so that the overall time dependence of P(x,t) is proportional to t^{-5/4}, and the scaling function g(u) has the limiting dependences g(u) approaching a constant as u--->0 and g(u)~exp(-u^{4/3}) as u--->infinity. This argument also suggests an effective continuum equation of motion for the infinite system which reproduces the correct asymptotic longitudinal probability distribution.

Random Response to Flow-Induced Forces

The response statistics of a linear structure subjected to excitation induced by a random flow with a non zero-mean velocity is examined. The technique of statistical linearization is applied on the nonlinear equation of motion of the structure. Approximate solutions for the structural response statistics are obtained. The Pierson-Moskowite is used to described the energy versus frequency distribution of the randomly flucuating component of the fluid motions. Results of several studies regarding parameters such as the fluid density and the structural stiffness are presented. The accuracy and efficiency of the analytical approach is assessed by comparison with data obtained by Monte Carlo simulations of the random structural response.

Functional Integration Theory for Incompressible Fluid Turbulence

A purely deductive approximation theory for incompressible fluid turbulence is presented, based exclusively on the Hopf characteristic functional space-time formulation and without any additive statistical postulate. Certain real symmetric solenoidal tensors called ``stationary functionalities'' are defined in terms of the characteristic functional by functional integration, quantities which vanish in the neighborhood of an exact physical characteristic functional, hence, for an approximate physical characteristic functional. By explicit functional integration, the first and second tensorial rank stationary functionalities are evaluated with a zero-mean velocity field Gaussian approximation for the characteristic functional. Equating the resulting expressions to zero produces a subsidiary equation and a dynamical equation for the two-point velocity correlation tensor, equations which are identical to the Navier-Stokes expectation value equation for a zero-mean velocity field and to a specific two-point Navier-Stokes expectation value equation with a zero-mean velocity field probability distribution such that the fourth-order velocity field product expectation values are related to lower-order product expectation values in the same way as for a zero-mean Gaussian probability distribution. Specialized forms of the nonlinear integrodifferential dynamical equation are worked out for the cases of homogeneous and isotropic homogeneous turbulence.