Axisymmetric Shear Flow Research Articles

Fabrication of a multi-stage plasma synthetic jet actuator using printed electronics

A new concept of electrode shape and arrangement is proposed to develop a multi-stage plasma synthetic jet actuator for the low-voltage operation. Exposed and covered electrodes, which have complicated shapes due to electrical wiring to the inner side of annular electrodes, are fabricated by an inkjet printing process using a silver nanoparticle-based ink. The plasma synthetic jet actuator developed in this study can be operated at 1000 V or lower. The discharge spreads uniformly from only the inner side of each annular electrode, inducing a unidirectional ionic wind toward the center of the coaxial electrode circle. Particle image velocimetry measurements reveal that the wall-normal jet induced by the multi-stage plasma synthetic jet actuator can be characterized as an axisymmetric free shear flow. The electrical and mechanical characteristics are similar to the linear-type dielectric-barrier-discharge plasma actuators. We also demonstrate that the printed electronics technique is suitable for the generation of arbitrary electrode shapes and arrangements and hence is a powerful tool for the realization of industrial applications of active airflow control devices using atmospheric pressure discharge.

An Analytically Derived Shear Stress and Kinetic Energy Equation for One-Equation Modelling of Complex Turbulent Flows

The Reynolds stress equations for two-dimensional and axisymmetric turbulent shear flows are simplified by invoking local equilibrium and boundary layer approximations in the near-wall region. These equations are made determinate by appropriately modelling the pressure–velocity correlation and dissipation rate terms and solved analytically to give a relation between the turbulent shear stress τ/ρ and the kinetic energy of turbulence (k=q2/2). This is derived without external body force present. The result is identical to that proposed by Nevzgljadov in A Phenomenological Theory of Turbulence, who formulated it through phenomenological arguments based on atmospheric boundary layer measurements. The analytical approach is extended to treat turbulent flows with external body forces. A general relation τ/ρ=a11−AFRiFq2/2 is obtained for these flows, where FRiF is a function of the gradient Richardson number RiF, and a1 is found to depend on turbulence models and their assumed constants. One set of constants yields a1= 0.378, while another gives a1= 0.328. With no body force, F ≡ 1 and the relation reduces to the Nevzgljadov equation with a1 determined to be either 0.378 or 0.328, depending on model constants set assumed. The present study suggests that 0.328 is in line with Nevzgljadov’s proposal. Thus, the present approach provides a theoretical base to evaluate the turbulent shear stress for flows with external body forces. The result is used to reduce the k–ε model to a one-equation model that solves the k-equation, the shear stress and kinetic energy equation, and an ε evaluated by assuming isotropic eddy viscosity behavior.

Stewartson-layer instability in a wide-gap spherical Couette experiment: Rossby number dependence

Instabilities of a viscous fluid between two fast but differentially rotating concentric spheres, the so-called spherical Couette flow, with a fixed radius ratio of $\unicode[STIX]{x1D702}=r_{i}/r_{o}=1/3$ are studied, where $r_{i}$ is the inner and $r_{o}$ the outer radius of the spherical shell. Of particular interest is the difference between cases where the Rossby number $Ro=(\unicode[STIX]{x1D6FA}_{i}-\unicode[STIX]{x1D6FA}_{o})/\unicode[STIX]{x1D6FA}_{o}>0$ and cases with $Ro<0$, where $\unicode[STIX]{x1D6FA}_{i}$ and $\unicode[STIX]{x1D6FA}_{o}$ are the inner- and outer-sphere angular velocities. The basic state in both situations is an axisymmetric shear flow with a Stewartson layer situated on the tangent cylinder. The tangent cylinder is given by a cylinder that touches the equator of the inner sphere with an axis parallel to the axis of rotation. The experimental results presented fully confirm earlier numerical results obtained by Hollerbach (J. Fluid Mech., vol. 492, 2003, pp. 289–302) showing that for $Ro>0$ a progression to higher azimuthal wavenumbers $m$ can be seen as the rotation rate $\unicode[STIX]{x1D6FA}_{0}$ increases, but $Ro<0$ gives $m=1$ over a large range of rotation rates. It is further found that in the former case the modes have spiral structures radiating away from Stewartson layer towards the outer shell whereas for $Ro<0$ the modes are trapped in the vicinity of the Stewartson layer. Further, the mean flow excited by inertial mode self-interaction and its correlation with the mode’s amplitudes are investigated. The scaling of the critical $Ro$ with Ekman number $E=\unicode[STIX]{x1D708}/(\unicode[STIX]{x1D6FA}_{o}\,d^{2})$, where $\unicode[STIX]{x1D708}$ is the kinematic viscosity and $d$ the gap width, is well within the bounds that have been established in a number of experimental studies using cylindrical geometries and numerical studies using spherical cavities. However, the present work is the first that experimentally examines Stewartson-layer instabilities as a function of the sign of $Ro$ for the true spherical-shell geometry.

Alternative depth-averaged models for gravity currents and free shear flows

Two approaches have traditionally been used to describe the widening rate of jets and plumes: the diffusion concept of Prandtl, and the entrainment principle of Morton, Taylor and Turner. The entrainment concept is based on depth-averaged flow scales, and was later applied to plane gravity currents on an incline by Ellison and Turner [ET]. The two parameterizations are compared here for free shear flows, and gravity currents. It is shown that the diffusion concept is suitable for supercritical gravity currents, and that both approaches agree for subcritical ones. Depth-averaged models are also used for open channel flows, but the depth and velocity scales for the two flows are different. Those of ET are derived from the velocity distribution, whereas the depth of an open channel flow is the vertical extent of the dense liquid phase, and the velocity is derived from its flux. To reconcile the two descriptions, we extended the mass-based flow scales of open channel flows to gravity currents in an earlier contribution. In the present study these scales are outlined, and extended further to axisymmetric and non-buoyant free shear flows. Ratios of the diffusion rates in terms of mass- and velocity-based flow scales, are obtained from available experimental data for free shear flows.

Linear stability of a compressible coaxial jet with continuous velocity and temperature profiles

This paper describes an investigation of the stability of a jet with velocity and temperature profiles characteristic of the exit region for a turbofan engine. Because the bypass stream mixes with both the exhaust and the ambient air, these profiles contain thin layers in which the velocity and temperature may vary rapidly. As a consequence, multiple instability modes are possible. In accordance with Rayleigh’s theorem for axisymmetric incompressible shear flows, it turns out that there are three possible modes, only two of which are unstable. We consider the effect on spatial growth rates of varying the diameter and velocity ratios, compressibility, and azimuthal wavenumber. Radiating modes, that are possible when the primary jet is heated, are also studied.

A formulation for calculating the translational velocity of a vortex ring or pair

Cephalopods, among other marine animals, use jet propulsion for swimming. A simple actuator is designed to loosely mimic pulsatile jet formation in squid and jellyfish. The actuator is comprised of a cavity with an oscillating diaphragm and an exit orifice. Periodic oscillation of the diaphragm results in the formation of an array of vortex rings and eventually could generate a periodic pulsatile jet. A general formulation for calculating the velocity of a steadily translating vortical structure in two-dimensional and axi-symmetric shear flows is presented. This technique is based on taking the variational derivative of an energetic function at its critical point. This technique is general, applicable to vortices in liquid and gas media, with no limitation on the relative size of the vortex core. The technique is then implemented to estimate the translational velocity of a vortex ring in a Helmholtz vortex ring generator.

Bifurcations, transitions, and attractors of real open flows

In this study, some dynamics that can be referred to as bifurcations, transitions, and attractors of real open flows, including axisymmetric shear flows, variable density jets, and wakes, have been presented. All of them can be considered as the experimental evidences of the quite abundant dynamics of the Navier-Stokes equations. A concept termed as physical territorial attractor (PTA) is proposed according to the properties of real open flows. Spatial evolutions of open flows, subsequently, can be described by different kinds of PTAs. Global relations through which global dynamics within one PTA or different PTAs can be studied are briefly introduced.

Mass and heat transfer during solid sphere dissolution in a non-uniform fluid flow

We studied a nonisothermal dissolution of a solvable solid spherical particle in an axisymmetric non-uniform fluid flow when the concentration level of the solute in the solvent is finite (finite dilution of solute approximation). It is shown that simultaneous heat and mass transfer during solid sphere dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with a parabolic velocity profile can be described by a system of generalized equations of convective diffusion and energy. Solutions of diffusion and energy equations are obtained in an exact analytical form. Using a general solution the asymptotic solutions for heat and mass transfer problem during spherical solid particle dissolution in a uniform fluid flow, axisymmetric shear flow, shear-translational flow and flow with parabolic velocity profile are derived. Theoretical results are in compliance with the available experimental data on falling urea particles dissolution in water and for solid sphere dissolution in a shear flow.

Coherent structures in countercurrent axisymmetric shear flows

The dynamical behaviors of coherent structures in countercurrent axisymmetric shear flows are experimentally studied. The forward velocityU1 and the velocity rationR=(U1-U2)/(U1+U2), whereU2 denotes the suction velocity, are considered as the control parameters. Two kinds of vortex structures, i.e., axisymmetric and helical structures, were discovered with respect to different regimes in theR versusU1 diagram. In the case ofU1 ranging from 3 to 20m/s andR from 1 to 3, the axisymmetric structures play an important role. Based on the dynamical behaviors of axisymmetric structures, a critical forward velocityU1cr=6.8m/s was defined, subsequently, the subcritical velocity regime:U1>U1cr and the supercritical velocity regime:U1 4m/s), correspondingly, the spatial evolution of the temporal asymptotic behavior of a dynamical system can be described as follows: (1) Hopf bifurcation, (2) subharmonic bifurcation, (3) reversed superharmonic bifurcation, (4) superharmonic bifurcation, (5) chaos (“weak turbulence”) in the case ofU1 4m/s). The proposed new terms, superharmonic and reversed superharmonic bifurcations, are characterized of the frequency doubling rather than the period doubling. A kind of unfamiliar vortices referred to as the helical structure was discovered experimentally when the forward velocity around 2m/s and the velocity range from 1.1 to 2.3. There are two base frequencies contained in the flow system and they could coexist as indicated by the Wigner-Ville-Distribution and the temporal asymptotic behavior of the dynamical system corresponding to the helical vortex could be described as 2-torus as indicted by the 3D reconstructed phase trajectory and correlation dimension. The scenario of the spatial evolution of helical structures could be described as follows: the jet column is separated into two parts at a certain spatial location and they entangle each other to form the helical vortex until the occurrence of those separated jet columns to reconnect further downstream with the result that the flow system evolves into turbulence in a catastrophic form. Correspondingly, the dynamical system evolves directly into 2-torus through the supercritical Hopf bifurcation followed by a transition from a quasi-periodic attractor to a strange attractor. In the case ofU1=2m/s, the parametric evolution of the temporal asymptotic behavior of the dynamical system as the velocity ratio increases from 1 to 3 could be described as follows: (1) 2-torus (Hopf bifurcation), (2) limit cycle (reversed Hopf bifurcation), (3) strange attractor (subharmonic bifurcation).

An experimental study on the coherent structures and chaotic phenomena in the axisymmetric countercurrent shear flow

The coherent structures and the chaotic phenomena in the transition of the axisymmetric countercurrent mixing shear flow were investigated experimentally. Two kinds of self-excited oscillation modes could exist in the axisymmetric countercurrent mixing shear flow. One is the shear layer self-excited oscillation mode corresponding to the high Reynolds number regime and the other is the jet column self-excited oscillation mode corresponding to the low Reynolds number regime in the case of the velocity ratio ranging from 1 to 1.5. Analyzing the auto-power spectrum, self-correlation-function and three dimensional reconstructed phase trajectory, the route to chaos through three Hopf bifurcations intercepted by an intermittency of the dynamical system corresponding to the axisymmetric countercurrent mixing shear flow was discovered when the velocity ratio is equal to 1.32.

SHEAR LAYER REFRACTION CORRECTIONS FOR OFF-AXIS SOURCES IN A JET FLOW

A set of equations is derived for converting acoustic measurements taken in a free-jet flight simulation facility, such as the U.K. Noise Test Facility at Pyestock or the French CEPRA-19 wind tunnel at Saclay, to equivalent farfield flight conditions. The equations are based on the high-frequency geometrical acoustics approximation, whose application in the present context was justified in early studies by Morfey and Tester in 1977 and by Amiet in 1978. However, the present work differs by allowing the source to be positioned off the jet centreline, anywhere within the flight stream. The flight stream jet is modelled as an axisymmetric parallel shear flow, with a shear layer thickness which is small compared with the jet diameter. The model also permits the microphone to be located anywhere outside the flow, arbitrarily close to the open jet. The consequences of off-axis source location are illustrated by numerical calculations.

Application of a nonlinear stress-strain model to axisymmetric turbulent swirling flows

A nonlinear stress-strain relation (NLSM) for the turbulence stresses is applied to axisymmetric free shear flows with and without swirl. This relation is an explicit solution to an algebraic Reynolds stress model (ARSIVI). The stress relation is a finite sum of tensor groups depicting various interactions between the mean strain and vorticity fields. Implementation is in the context of a k−e type model. Comparisons are made between flow field predictions obtained with the full Reynolds stress model, the NLSM corresponding to improved and standard ARSMs, the k−e model and experimental data.

Unified turbulence closure model for axisymmetric and planar free shear flows

A new two-equation turbulence model based on the exact turbulent kinetic energy and the variance of vorticity or enstrophy equations is developed and used to calculate planar and axisymmetric free shear flows. It is shown that one set of model constants reproduces available growth rates and similarity profiles of velocity and shear stress. In general, agreement is well within the scatter of experimental data.

Drag coefficient of a gas bubble in an axisymmetric shear flow

The drag coefficient of a gas bubble in steady motion in an unbounded axisymmetric shear flow is obtained numerically for different values of the Reynolds and Weber numbers.

Preferential concentration of particles by turbulence

Preferential concentration describes the accumulation of dense particles within specific regions of the instantaneous turbulence field. This phenomenon occurs in dilute particle-laden flows with particle time constants of the same order as an appropriately chosen turbulence time scale. The mechanisms which drive preferential concentration are centrifuging of particles away from vortex cores and accumulation of particles in convergence zones. Experimental and numerical studies are reviewed which demonstrate that preferential concentration occurs in a wide range of flows including plane and axisymmetric free shear flows, wall-bounded flows, homogeneous turbulent flows, and complex shear flows. The same basic mechanisms are active in all these flows but the specific effects and the definition of an appropriate time scale change from problem to problem. Preferential concentration has been shown to have a significant effect on droplet combustion, aerosol particle settling and turbulence modification by particles and is expected to be significant in numerous other applications. Current models describing preferential concentration and its global effects on the flow are inadequate.

Noncircular jets in combustion systems

Combustion dynamics of burners with corners were studied using Planar Laser Induced Fluorescence (PLIF) imaging. The effect of sharp corners on the air flow dynamics, shown earlier in cold flow tests, was also found in the reacting flow of a flame. The sharp corners interrupted the coherent structures generated in an axisymmetric shear flow. The combustion at the flat sections of the flame occurred in periodic, coherent large scale structures but was continuous and homogeneous in the vertices sections. The azimuthal structure of the noncircular flame changed in a pattern similar to that found in nonreacting flows. Combined regions of small- and large-scale mixing in the same flow, a unique feature of burners having sharp corners, is beneficial for combustion applications.

Axisymmetric shear flow over spheres and spheroids

Analytical solutions for an inviscid, incompressible, axisymmetric shear flow over a sphere are established. It is determined that if the shear is sufficiently large with respect to the axis velocity then a recirculating stagnation region is formed. Solutions for prolate and oblate spheroids exhibit the same flowfield characteristics as for the sphere. Stagnation bubble formation is delayed on the prolate spheroids and promoted on the oblate spheroids. These results are related to those for the two-dimensional shear flow over cylinders analyzed by Tsien (1943) and Fraenkel (1961).

Flow separation in a viscous parabolic shear past a sphere

Axisymmetric parabolic shear flow past a spinning sphere in an unbounded viscous medium is considered using the matching technique and taking the non-uniform shear as the dominant feature, where the Reynolds number based on parabolic shearRe≪1 and the rotational Reynolds number based on the angular rotation of the sphereR0≪1 are such thatR02/Re=O(1). Forces on the body are calculated and flow separation from the boundary is studied. Coalescion of two wakes or detachment of a wake into two are observed, depending on the increase in magnitudeU′ of the free stream for a fixedR02/Re or increase inR02/Re for a fixedU′ respectively.

Generation of vortices in an axisymmetric shear flow

Generation of vortices in an axisymmetric shear flow

Noise from an axisymmetric shear flow: II analytical results

Noise from an axisymmetric shear flow: II analytical results