Kinematic Viscosity Of Fluid Research Articles

Numerical investigation of flow-induced rotary oscillation of circular cylinder with rigid splitter plate

Numerical results of fluid flow over a rotationally oscillating circular cylinder with splitter plate are presented here. Different from the previous examinations with freely rotatable assembly, the fluid and structure interactions are treated as a coupled dynamic system by fully considering the structural inertia, stiffness, and damping. The hydrodynamic characteristics are examined in terms of reduced velocity Ur at a relatively low Reynolds number Re = 100 for different plate lengths of L/D = 0.5, 1.0, and 1.5, where Ur = U/(Dfn), Re = UD/υ and fn = (κ/J)0.5/2π with U the free stream velocity, D the diameter of the circular cylinder, υ the fluid kinematic viscosity, fn the natural frequency, J the inertial moment, κ the torsional stiffness, and L the plate length. Contrast to the freely rotating cylinder/plate body, that is, in the limit of κ → 0 or Ur →∞, remarkable rotary oscillation is observed at relatively low reduced velocities. For the typical case with L/D = 1.0, the maximum amplitude may reach five times that at the highest reduced velocity of Ur = 15.0 considered in this work. At the critical reduced velocity Ur = 4.2, notable hydrodynamic jumps are identified for the rotation amplitude, response frequency, mean drag coefficient, lift amplitude, and vortex shedding frequency. Moreover, the phase angle between the fluid moment and rotary oscillation abruptly changes from 0 to π at Ur = 6.5. Due to the combined effect of fluid moment, rotation response, and phase difference, the natural frequency of the rotating body varies in flow, leading to a wide regime of lock-in/synchronization (Ur ≥4.2, for L/D = 1.0). The phenomenon of rotation bifurcation, i.e., the equilibrium position of the rotary oscillation deflects to a position which is not parallel to the free stream, is found to only occur at higher reduced velocities. The longer splitter plate has the lower critical reduced velocity. The occurrence of bifurcation is attributed to the anti-symmetry breaking of the wake flow evolution. The resultant asymmetric mean pressure distribution on the splitter plate gives rise to the net lift force and the deviated moment on the assembly, leading to the offset mean position of splitter plate. The global vortex shedding is identified to be the classic 2S mode for both cases with and without the bifurcation, although the second vortex formation and the shedding pattern in the near wake for the bifurcate case are different from the non-bifurcate case with lower reduced velocities.

Optimization of Single-Trip Milling Using Large-Diameter Coiled Tubing

This article, written by Special Publications Editor Adam Wilson, contains highlights of paper SPE 179090, “Optimization of Single-Trip Milling Using 2-in. Coiled Tubing,” by Elizabeth Snyder, SPE, and Justin Noland, SPE, Sanjel, prepared for the 2016 SPE/ICoTA Coiled Tubing and Well Intervention Conference and Exhibition, Houston, 22–23 March. The paper has not been peer reviewed. Larger-diameter coiled tubing (CT) recently has been used to perform millouts because of its improved setdown force and increased annular velocities (AVs) for cleanout purposes. Service companies and operators have reduced the number of wiper trips when using larger-diameter CT, to save time and money. Milling efficiency using 2-in. CT can be dramatically improved by maintaining proper fluid rheology throughout the operation. By doing so, 2-in. CT has been used to perform single-trip millouts, reducing operational time by 40%. Fluids The main objective of CT operations in horizontal wells is to clean the lateral completely of any debris without compromising the well’s integrity. The first and most important component of single-trip-millout operations is correct fluid rheology. This system comprises the AV, Reynolds number (RE), and fluid viscosity. With correct use of chemicals and proper AVs, the fluid system allows sand and debris to travel out of the wellbore. The RE determines the flow regime as laminar, transitional, or turbulent. Turbulent flow is characterized by swirling of the water (i.e., presence of eddies), which agitates the settling bed, enabling sand and debris to flow out of the lateral and, in turn, out of the well. RE can be broken into three components: fluid velocity, hydraulic diameter (flow area between casing and coil), and kinematic viscosity (funnel viscosity). In this case, the hydraulic diameter is predetermined by the 2-in. CT working in 7- to 4.5-in. cased wells, leaving the velocity and viscosity dependent on each operation. When pumping any treatment fluid through CT, a fluid friction reducer (FR) must be pumped continuously to reduce friction pressure generated from pumping fluid through a restricted area. The FR decreases the circulating pressure, enabling higher pump rates to be achieved. A rheology-control unit uses electric variable-frequency-drive pumps to add FR and other chemicals to the fluid and to provide the ability to change dosage on the fly. These pumps are accurate down to thousandths of a gallon, enabling higher chemical usage in smaller doses. The chemicals are injected directly into the flow, then inline mixers enable shearing of the chemical to attain consistent mixing. Direct injection and inline mixers eliminate the unnecessary waste and oversaturation of chemicals seen when using conventional mixing tubs. This optimized fluid increases the longevity of the recirculated water while maintaining a high RE, in turn decreasing the cost to the operator. Another common practice of conventional millouts was to send multiple linear-gel sweeps throughout the lateral. The objective was to increase the viscosity of the fluid to lift sand and debris out of the well. However, it has been discovered that the more-viscous-gel sweeps lead to laminar flow, which is not conducive to moving sand and debris in the lateral. The laminar fluid flows over debris, enabling it to settle and stay in the lateral section of the well. Gel sweeps have viscosities of 20 cp or greater, compromising the RE down to below 20,000. Because the viscosity is high and the RE is too low to transport sand and debris, gel sweeps were limited during optimized single-trip millouts.

Variations of bed elevations due to turbulence around submerged cylinder in sand beds

This paper presents the spatio-temporal variations in bed elevations and the near-bed turbulence statistics over the deformed bed generated around the submerged cylindrical piers embedded vertically on loose sediment bed at a constant flow discharge. Experiments were carried out in a laboratory flume for three blockage ratios in the range of 0.04–0.06 using three different sizes of submerged cylinders individually placed vertically at the centerline of the flume. Clear-water experimental conditions were maintained over the smooth sediment bed surface with a constant flow discharge (\(Q = 0.015\,{\rm m}^3/{\rm sec}\)), thereby giving three different cylinder Reynolds numbers \(Re_{D_c} = \frac{U_mD_c}{\nu }\) (=10200, 12750, 15300) away from the cylinder locations, where \(U_m\) is the maximum mean velocity, \(D_c\) is the cylinder diameter and \(\nu\) is the kinematic viscosity of fluid. Instantaneous sand bed elevations around the cylinders were recorded using a SeaTek 5MHz ultrasonic ranging system of net 24 transducers to estimate bed form migration, and the near-bed velocity data at transducer locations over the stable deformed bed around the pier-like structures were collected using down-looking three-dimensional (3D) Micro-acoustic Doppler velocimeter to estimate the bottom Reynolds shear stresses and the contributions of bursting events to the dominant shear stress component. The flow perturbation generated due to relatively lower flow blockage ratio favored to achieve the stable bed condition more rapidly than the others, and larger upstream scour-depth and deformed areas were noticed for greater flow blockage ratio due to larger cylinder diameter. For larger blockage ratio in the upstream of scour-hole near the bed, occurrences of probabilities of both boundary-ward interactions (Q1 and Q3) were the dominant; whereas in the downstream of the scoured region, occurrences of probabilities of second and third quadrant events (Q2 and Q4) were dominant. On the other hand, for the lower blockage ratio, quadrant (Q2) was dominant over Q4 in the downstream of scour-hole, and in the upstream of scour-hole, quadrant Q4 was the dominant.

Strong-field spherical dynamos

Numerical models of the geodynamo are usually classified into two categories: dipolar modes, observed when the inertial term is small enough; and multipolar fluctuating dynamos, for stronger forcing. We show that a third dynamo branch corresponding to a dominant force balance between the Coriolis force and the Lorentz force can be produced numerically. This force balance is usually referred to as the strong-field limit. This solution coexists with the often described viscous branch. Direct numerical simulations exhibit a transition from a weak-field dynamo branch, in which viscous effects set the dominant length scale, and the strong-field branch, in which viscous and inertial effects are largely negligible. These results indicate that a distinguished limit needs to be sought to produce numerical models relevant to the geodynamo and that the usual approach of minimising the magnetic Prandtl number (ratio of the fluid kinematic viscosity to its magnetic diffusivity) at a given Ekman number is misleading.

Dependence on aspect ratio of symmetry breaking for oscillating foils: implications for flapping flight

Using two-dimensional direct numerical simulations, we investigate the flow in a fluid of kinematic viscosity ${\it\nu}$ and density ${\it\rho}$ around elliptical foils of density ${\it\rho}_{s}$ with major axis $c$ and minor axis $b$ for three different aspect ratios: $AR=b/c=1$ (a circle); $AR=0.5$; and $AR=0.1$. The vertical location of these foils $y_{s}(t)=A\sin (2{\rm\pi}f_{0}t)$ oscillates with amplitude $A$ and frequency $f_{0}$ in two distinct ways: ‘pure’ oscillation, where the foils are constrained to remain in place; and ‘flying’ oscillation, where horizontal motion is allowed. We simulate the flow for a range of the two appropriate control parameters, the non-dimensional amplitude, or Keulegan–Carpenter number $KC=2{\rm\pi}A/c$, and the non-dimensional frequency, or Stokes number ${\it\beta}=f_{0}c^{2}/{\it\nu}$. We observe three distinct patterns of asymmetry, labelled ‘S-type’ for synchronous asymmetry, ‘$\text{QP}_{\text{H}}$-type’ and ‘$\text{QP}_{\text{L}}$-type’ for quasi-periodic asymmetry at sufficiently high and sufficiently low (i.e. $AR=0.1$) aspect ratios, respectively. These patterns are separated at the critical locus in $KC$–${\it\beta}$ space by a ‘freezing point’ where the two incommensurate frequencies of the QP-type flows combine, and we show that this freezing point tends to occur at smaller values of $KC$ as $AR$ decreases. We find for the smallest aspect ratio case ($AR=0.1$) that the transition to asymmetry, for all values of $KC$, occurs for a critical value of an ‘amplitude’ Stokes number ${\it\beta}_{A}={\it\beta}(KC)^{2}=4{\rm\pi}^{2}f_{0}A^{2}/{\it\nu}\simeq 3$. The $\text{QP}_{\text{L}}$-type asymmetry for $AR=0.1$ is qualitatively different in physical and mathematical structure from the $\text{QP}_{\text{H}}$-type asymmetry at higher aspect ratio. The flows at the two ends of the ellipse become essentially decoupled from each other for the $\text{QP}_{\text{L}}$-type asymmetry, the two frequencies in the horizontal force signature being close to the primary frequency, rather than twice the primary frequency as in the $\text{QP}_{\text{H}}$-type asymmetry. Furthermore, the associated coefficients arising from a Floquet stability analysis close to the critical thresholds are profoundly different for low aspect ratio foils. Freedom to move slightly suppresses the transition to S-type asymmetry, and for certain parameters, if a purely oscillating foil subject to S-type asymmetry is released to move, flow symmetry is rapidly recovered due to the negative feedback of small horizontal foil motion. Conversely, for the ‘higher’ aspect ratios, the transition to $\text{QP}_{\text{H}}$-type asymmetry is encouraged when the foil is allowed to move, with strong positive feedback occurring between the shed vortices from successive oscillation cycles. For $AR=0.1$, freedom to move significantly encourages the onset of asymmetry, but the newly observed ‘primary’ $\text{QP}_{\text{L}}$-type asymmetry found for pure oscillation no longer occurs when the foil flies, with S-type asymmetry leading ultimately to locomotion at a constant speed occurring all along the transition boundary for all values of $KC$ and ${\it\beta}$.

Preferred interparticle spacings in trains of particles in inertial microchannel flows

Suspended particles migrate towards inertial focusing positions close to walls and align into trains in finite inertia conduit flow. The relative contribution of inertial and viscous forces at the particle length scale, defined by the particle Reynolds number ($\mathit{Re}_{p}$), is a key parameter, where $\mathit{Re}_{p}=\langle \dot{\unicode[STIX]{x1D6FE}}\rangle D^{2}/\unicode[STIX]{x1D708}$ depends on the mean shear rate $\langle \dot{\unicode[STIX]{x1D6FE}}\rangle$, particle diameter $D$ and fluid kinematic viscosity $\unicode[STIX]{x1D708}$. Controlling the location of inertial focusing positions and the interparticle distance is critical in applications such as flow cytometry, imaging and cell entrapment in droplets. By using experimental observations in rectangular microchannels and lattice Boltzmann numerical simulations of dilute suspension flow, the spacing between particles aligned in trains is measured. From the modes of the probability density function of interparticle spacing, preferred spacings at $5D$ and $2.5D$ are observed. At lower $\mathit{Re}_{p}$, the preferred spacing forms around $5D$, and with increasing $\mathit{Re}_{p}$ the spacing at $2.5D$ becomes more pronounced. With increasing concentration of the suspension the spacing is influenced by particle crowding effects until stable trains are no longer observed.

Parameter analysis of water flow during EPBS tunnelling and an evaluation method of spewing failure based on a simplified model

Spewing failure always occurs when a tunnel is constructed in water-rich sand stratum using an earth pressure balance shield, which could lead to considerable disturbance of the environment. However, few studies have investigated the mechanism of spewing. To understand the mechanism of screw conveyor spewing, a new simplified model was proposed to calculate the groundwater flow rate and water pressure gradient in the earth pressure balance shield. Ergun’s equation was used to consider the influence of turbulent flow, which is inevitable during spewing. The model was verified by tests, and a parameter analysis was conducted to investigate the effects of soil behaviour, fluid kinematic viscosity and shield geometry. Additionally, an evaluation method to predict spewing was proposed based on the simplified model, and the method was verified by investigating real-world engineering problems. The results indicate that the groundwater flow rate and velocity in the screw conveyor increase significantly with increasing soil hydraulic conductivity in the turbulent flow range. The influence of soil porosity on the groundwater flow rate and velocity is greater than that of the soil’s average particle diameter. In addition, increasing the screw conveyor length can be used to control spewing. Comparisons with practical engineering examples show that the proposed method is effective. The proposed method can be used to predict the risk of spewing such that appropriate measures can be taken.

Effects of inertia and viscoelasticity on sedimenting anisotropic particles

An axisymmetric particle sedimenting in an otherwise quiescent Newtonian fluid, in the Stokes regime, retains its initial orientation. For the special case of a spheroidal geometry, we examine analytically the effects of weak inertia and viscoelasticity in driving the particle towards an eventual steady orientation independent of initial conditions. The generalized reciprocal theorem, together with a novel vector spheroidal harmonics formalism, is used to find closed-form analytical expressions for the$O(\mathit{Re})$inertial torque and the$O(\mathit{De})$viscoelastic torque acting on a sedimenting spheroid of an arbitrary aspect ratio. Here,$\mathit{Re}=UL/{\it\nu}$is the Reynolds number, with$U$being the sedimentation velocity,$L$the semi-major axis and${\it\nu}$the fluid kinematic viscosity, and is a measure of the inertial forces acting at the particle scale. The Deborah number,$\mathit{De}=({\it\lambda}U)/L$, is a dimensionless measure of the fluid viscoelasticity, with${\it\lambda}$being the intrinsic relaxation time of the underlying microstructure. The analysis is valid in the limit$\mathit{Re},\mathit{De}\ll 1$, and the effects of viscoelasticity are therefore modelled using the constitutive equation of a second-order fluid. The inertial torque always acts to turn the spheroid broadside-on, while the final orientation due to the viscoelastic torque depends on the ratio of the magnitude of the first ($N_{1}$) to the second normal stress difference ($N_{2}$), and the sign (tensile or compressive) of$N_{1}$. For the usual case of near-equilibrium complex fluids – a positive and dominant$N_{1}$($N_{1}>0$,$N_{2}<0$and$|N_{1}/N_{2}|>1$) – both prolate and oblate spheroids adopt a longside-on orientation. The viscoelastic torque is found to be remarkably sensitive to variations in${\it\kappa}$in the slender-fibre limit (${\it\kappa}\gg 1$), where${\it\kappa}=L/b$is the aspect ratio,$b$being the radius of the spheroid (semi-minor axis). The angular dependence of the inertial and viscoelastic torques turn out to be identical, and one may then characterize the long-time orientation of the sedimenting spheroid based solely on a critical value ($\mathit{El}_{c}$) of the elasticity number,$\mathit{El}=\mathit{De}/\mathit{Re}$. For$\mathit{El}<\mathit{El}_{c}~({>}\mathit{El}_{c})$, inertia (viscoelasticity) prevails with the spheroid settling broadside-on (longside-on). The analysis shows that$\mathit{El}_{c}\sim O[(1/\text{ln}\,{\it\kappa})]$for${\it\kappa}\gg 1$, and the viscoelastic torque thus dominates for a slender rigid fibre. For a slender fibre alone, we also briefly analyse the effects of elasticity on fibre orientation outside the second-order fluid regime.

Effect of noncircular orifice plates on the near flow field of turbulent free jets

In this paper, we experimentally investigate the near-field flow characteristics of turbulent free jets respectively issued from circular, triangular, diamond, rectangular, and notched-rectangular orifice plates into air surroundings. All the orifice plates have identical opening areas or equivalent diameters (De) and their aspect ratios (AR) range from 1 to 6.5. Planar particle image velocimetry (PIV) is used to measure the velocity field at the same Reynolds number of Re = 5 × 104, where Re = UeDe/v with Ue being the exit bulk velocity and v the kinematic viscosity of fluid. The mean and turbulent velocity fields of all the five jets are compared in detail. Results show that the noncircular jets can enhance the entrainment rate, reflected by the higher acceleration rates of mean velocity decay and spread, shorten the length of the unmixed core, expedite the increase of turbulent intensity compared with the circular counterpart shortened unmixed core, and increase turbulent intensity comparing to the circular counterpart. Among the five jets, the rectangular jet (AR = 6.5) produces the greatest decay rate of the near-field mean velocity, postpones the position at which the `axis-switching' phenomenon occurs. This supports that axis switching phenomenon strongly depends on jet initial conditions. In addition, the hump in the centerline variation of the turbulence intensity is observed in the rectangular and triangular jets, but not in the circular jet, nor in diamond jet nor in notched-rectangular jet.

Taylor dispersion in oscillatory flow in rectangular channels

This paper focuses on exploring the effect of the side walls on dispersion in oscillatory Poiseuille flows in rectangular channels. The method of multiple time scales with regular expansions is utilized to obtain analytical expressions for the effective dispersivity D3D⁎. The dispersion coefficient is of the form D3D⁎/Pe2=f(Ω≡ωh2/D,Sc≡D/ν,χ≡w/h) where Pe≡<u>h/D, <u> is the root mean square of the cross-section averaged velocity, ω is the angular velocity, 2w and 2h are, respectively, the width and the height of the cross-section, D is the solute diffusivity, and ν is the fluid kinematic viscosity. The analytical results are compared with full numerical simulations and asymptotic expressions. Also effect of various parameters on dispersion coefficient is explored. For small oscillation frequency Ω the dispersion coefficient approaches the time averaged dispersion of the Poiseuille flow and for large Ω, D3D⁎ scales as Pe2/Ω2 where Pe=<u>h/D. Due to its relative simplicity, the 2D model is frequently utilized for calculating dispersion in channels. However at small dimensionless frequencies the 2D model can significantly underestimate the dispersion, particularly for channels with large χ. At large Ω the dispersion coefficient predicted from the 2D model becomes reasonably accurate, particularly for channels with large χ. For a square channel, the 2D prediction is reasonably accurate for all frequencies. The results of this study will enhance our understanding of transport in microscale systems that are subjected to oscillating flows, and potentially aid technological advances in diverse areas relevant to microfluidic devices.

The history force on a small particle in a linearly stratified fluid

AbstractThe hydrodynamic force experienced by a small spherical particle undergoing an arbitrary time-dependent motion in a weakly density-stratified fluid is investigated theoretically. The study is carried out under the Oberbeck–Boussinesq approximation and in the limit of small Reynolds and small Péclet numbers. The force acting on the particle is obtained by using matched-asymptotic expansions. In this approach, the small parameter is given by$a/\ell $, where$a$is the particle radius and$\ell $is the stratification length, as defined by Ardekani &amp; Stocker (Phys. Rev. Lett., vol. 105, 2010, article 084502), which depends on the Brunt–Väisälä frequency, on the fluid kinematic viscosity and on the thermal or the concentration diffusivity (depending on the case considered). The matching procedure used here, which is based on series expansions of generalized functions, slightly differs from that generally used in similar problems. In addition to the classical Stokes drag, it is found that the particle experiences a memory force given by two convolution products, one of which involves, as usual, the particle acceleration and the other one, the particle velocity. Owing to the stratification, the transient behaviour of this memory force, in response to an abrupt motion, consists of an initial fast decrease followed by a damped oscillation with an angular frequency corresponding to the Brunt–Väisälä frequency. The perturbation force eventually tends to a constant which provides us with correction terms that should be added to the Stokes drag to accurately predict the settling time of a particle in a diffusive stratified fluid.

Numerical study of air jet flow field during a loss of vacuum

Air leakage into tokamaks vacuum vessel during plasma burning or maintenance operations may lead to the fast pressurization of the vacuum vessel. A fraction of the dust inventory present in the vacuum vessel can be mobilized threatening the safety of staff and workers on site, the local population and the environment. A numerical analysis of the physical phenomena involved in such accidents is necessary in order to predict the thermal-fluid dynamics into the vacuum vessel after air ingress and consequent dust mobilization. Accuracy of the numerical results is also required in order to provide a sufficient margin in the design of the safety systems. The numerical simulation of Loss of Vacuum Accident (LOVA) scenarios is a challenging task for today numerical methods and models because it involves large volumes, multiphase flows ranging from highly supersonic to nearly incompressible and contemporary heat transfer. The drag force exerted on the dust by a moving fluid due to the viscous surface shear stress and pressure distribution around the dust particles depends mainly on the Reynolds number, i.e. property of the fluid (kinematic viscosity), its mean velocity and characteristic length of the geometry. For a fixed geometry, the key parameter for the dust mobilization is the velocity field of the continuous phase, and its thermodynamics properties, inside the vacuum vessel. In this contribution, the authors present and discuss the results of numerical simulations of air jet flow field during a LOVA with particular attention to the comparison with the experimental data and differences arising from the use of different types of grid resolution and turbulence models (Zero-Equation, k–ω and SST).

Role of Local Flow Conditions in River Biofilm Colonization and Early Growth

AbstractDirect numerical simulations of a turbulent boundary layer flow over a bed of hemispheres of height h are performed using an immersed boundary method for comparison with river biofilm growth experiments performed in a hydraulic flume. Flow statistics above the substrates are shown to be in agreement with measurements performed by laser Doppler velocimetry and particle image velocimetry in the experiments. Numerical simulations give access to flow components inside the roughness sublayer, and biofilm colonization patterns found in the experiments are shown to be associated with low shear stress regions on the hemisphere surface. Two bed configurations, namely staggered and aligned configurations, lead to different colonization patterns because of differences in the local flow topology. Dependence with the Reynolds number of the biofilm distribution and accrual 7 days after inoculum is shown to be associated to local flow topology change and shear stress intensity. In particular, the shear stress τ on the surface of the hemispheres is found to scale as , where Ret = u*h/ν, with u* as the log law friction velocity and ν as the fluid kinematic viscosity. This scaling is due to the development of boundary layers along the hemisphere surface. Associated with a critical shear stress for colonization and early growth, it explains the increasing delay in biomass accrual for increasing flow velocities in the experiments. Copyright © 2014 John Wiley &amp; Sons, Ltd.

Analysis of the Navier-Stokes Equations

The Navier-Stokes equations for incompressible fluid flows with impervious boundary and free surface are analyzed by means of a perturbation procedure involving dimensionless variables and a dimensionless perturbation parameter which is composed of kinematic viscosity of fluid, the acceleration of gravity and a characteristic length. The new dimensionless variables are introduced into the equation system. In addition, the perturbation parameter is introduced into terms for deriving approximations systems of different orders. Such systems are obtained by equating coefficients of like powers of perturbation parameter for the successive coefficients in the series. In these systems several terms are analyzed with regards to size and significance. Based on those systems, suitable solutions of NS equations can be found for different boundary conditions. For example, a relation for stationary channel flow is obtained as approximation to the NS equations of the lowest order after transformation back to dimensional variables.

PIV measurements of turbulent jets issuing from triangular and circular orifice plates

The present study experimentally investigated the near-field flow mixing characteristics of two turbulent jets issuing from equilateral triangular and circular orifice plates into effectively unbounded surroundings, respectively. Planar particle image velocimetry (PIV) was applied to measure the velocity field at the same Reynolds number of Re=50,000, where Re = U e D e/ν with U e being the exit bulk velocity and ν the kinematic viscosity of fluid, D e the equivalent diameters. The instantaneous velocity, mean velocity, Reynolds stresses were obtained. From the mean velocity field, the centreline velocity decay rate and half-velocity width were derived. Comparing the mixing characteristics of the two jets, it is found that the triangular jet has a faster mixing rate than the circular counterpart. The triangular jet entrainments with the ambient fluid at a higher rate in the near field. This is evidenced by a shorter unmixed core, faster Reynolds stress and centreline turbulence intensity growth. The primary coherent structures in the near field are found to break down more rapidly in the triangular jet as compared to the circular jet. Over the entire measurement region, the triangular jet maintained a higher rate of decay and spread. Moreover, all components of Reynolds stress of the triangular jet appear to reach their peaks earlier, and then decay more rapidly than those of the circular jet. In addition, the axis-switching phenomenon is observed in the triangular jet.

Instability by Weak Precession of the Flow in a Rotating Sphere

A linear stability analysis is presented of the steady flow in a rapidly rotating sphere undergoing weak precession. It is well-known that without precession all disturbances damp with decay rate proportional to Re−1/2 where Re = a2Ωs/ν is the Reynolds num- ber defined by a the sphere radius, Ωs the the spin angular velocity, and ν the kinematic viscosity of fluid. With precession, two kinds of instability modes exist; one is global and inviscid in nature, and the other is local and viscous. Here we investigate the former by an asymptotic analysis for large Re and small Γ (= Ωp/Ωs), the ratio of the precession and spin angular velocities. It is shown that a weak precession with Γ of order Re−1/2 destabilises disturbances through coupling between an axisymmetric mode (with respect to the spin axis) and the (2,1,1) mode. We find that the neutral curve for the instability behaves asymptotically as Γ = 7.9Re−1/2. For the local modes on the other hand, the neutral curve behaves as Γ ∝ Re−4/5. These results are compared with observations (Goto et al., 2011) for a precessing sphere and spheroid.

0501 平板間クエット流における過渡的乱れの発生(OS5-1 壁乱流:統計,構造,動力学の理解,OS5 壁乱流:統計,構造,動力学の理解)

The onset of transient turbulence in plane Couette flow is identified as a homoclinic tangency with respect to a simple edge state for the Navier-Stokes equation, i.e., the gentle periodic orbit found by Kawahara & Kida (J. Fluid Mech., vol. 449, 2001, pp. 291-300). The tangency of a pair of distinct homoclinic orbits is numerically discovered at the critical Reynolds number Re ≡ Uh/ν = 241.3 (U, h, and ν being half the difference of the two wall velocities, half the wall separation, and the kinematic viscosity of fluid, respectively) above which transversal homoclinic points appear on the Poincar´e section to generate a transient chaos through a Smale horseshoe.

Comments on the paper “A study of induced magnetic field with chemically reacting and radiating fluid past a vertical permeable plate” by S. Ahmed

In the paper "A study of induced magnetic field with chemically reacting and radiating fluid past a vertical permeable plate" by S. Ahmed published in Journal of Engineering Physics and Thermophysics [1], the influence of thermal radiation and chemical reaction on the steady MHD heat and mass transfer by a mixed convective flow of a viscous, incompressible, electrically conducting Newtonian fluid past a vertical permeable plate with account for an induced magnetic field was investigated. The similarity solutions of the transformed nondimensional governing equations were obtained by the series expansion technique. All the results were presented for air and water at 20C with the Prandtl numbers equal to 0.71 and 7, respectively. The above work is of interest, but it has serious disadvantages, which will be analyzed below: 1. On p. 1363, the Eckert number Ec as a parameter is used. However, this parameter was not defined anywhere in the paper. Usually, this number is used when the viscous dissipation term is included into the energy equation. However, in the present problem no viscous dissipation term exists. 2. The assumption that, except for the applied external uniform magnetic field, a new magnetic field appears, which is induced by the electrically conducting fluid and which interacts with the external field, gives a fresh approach to the problem. However, the importance of the induced magnetic field depends on the magnetic Reynolds number defined [2] as Rm = μσul, where μ is the magnetic permeability, σ is the fluid electrical conductivity, u is the characteristic flow velocity, and l is the characteristic length scale. When the magnetic Reynolds number is much smaller than unity, the induced magnetic field is negligible, and the imposed external magnetic field is unaffected by the moving conducting fluid [2]. In most laboratory experiments or industrial processes, Rm is very low, being usually less than 10 [3]. In contrast, when the magnetic Reynolds number is equal to or greater than unity, the induced magnetic field is of importance and should be taken into account. Indeed, certain applications, such as advanced schemes for controlling magnetogasdynamic flows around hypersonic vehicles, involve the values of Rm in the range 1–10 [3]. In the discussed work [1], the author took into account the induced magnetic field without any reference to the magnetic Reynolds number that is the characteristic criterion. We can calculate Rm for air at 20 C. According to [4], at this temperature the electrical conductivity of air varies from 3⋅10 to 8⋅10 Ω⋅m, whereas the magnetic permeability is equal to 1.257⋅10 H/m [5]. For a typical velocity u = 1 m/ s and a typical length scale l = 0.1 m, the magnetic Reynolds number is Rm 3.8⋅10 . For water at 20C, σ = 10 Ω⋅m [6] and μ = 1.257⋅10 H/m [5]. Here, for typical velocity and length scale Rm = 1.257⋅10 . Instead of using the above-mentioned magnetic Reynolds number, the author of [1] used the parameter Pm, called the magnetic Prandtl number: Pm = σνμ, where ν is the fluid kinematic viscosity. In [1], all the results were obtained for air and water, which corresponds, in the author’s opinion, to Pm changing from 0.1 to 1. Let us calculate Pm for air at 20C. Here, ν = 1.827⋅10 m/s [7], so that we have Pm 6.9⋅10. For water ν = 9.8⋅10 m/s [7], and we obtain Pm = 1.23⋅10. Journal of Engineering Physics and Thermophysics, Vol. 86, No. 1, January, 2013

Fluvial features on Titan: Insights from morphology and modeling

Fluvial features on Titan have been identified in synthetic aperture radar (SAR) data taken during spacecraft flybys by the Cassini Titan Radar Mapper (RADAR) and in Descent Imager/Spectral Radiometer (DISR) images taken during descent of the Huygens probe to the surface. Interpretations using terrestrial analogs and process mechanics extend our perspective on fluvial geomorphology to another world and offer insight into their formative processes. At the landscape scale, the varied morphologies of Titan’s fluvial networks imply a variety of mechanical controls, including structural influence, on channelized flows. At the reach scale, the various morphologies of individual fluvial features, implying a broad range of fluvial processes, suggest that (paleo-)flows did not occupy the entire observed width of the features. DISR images provide a spatially limited view of uplands dissected by valley networks, also likely formed by overland flows, which are not visible in lower-resolution SAR data. This high-resolution snapshot suggests that some fluvial features observed in SAR data may be river valleys rather than channels, and that uplands elsewhere on Titan may also have fine-scale fluvial dissection that is not resolved in SAR data. Radar-bright terrain with crenulated bright and dark bands is hypothesized here to be a signature of fine-scale fluvial dissection. Fluvial deposition is inferred to occur in braided channels, in (paleo)lake basins, and on SAR-dark plains, and DISR images at the surface indicate the presence of fluvial sediment. Flow sufficient to move sediment is inferred from observations and modeling of atmospheric processes, which support the inference from surface morphology of precipitation-fed fluvial processes. With material properties appropriate for Titan, terrestrial hydraulic equations are applicable to flow on Titan for fully turbulent flow and rough boundaries. For low-Reynolds-number flow over smooth boundaries, however, knowledge of fluid kinematic viscosity is necessary. Sediment movement and bed form development should occur at lower bed shear stress on Titan than on Earth. Scaling bedrock erosion, however, is hampered by uncertainties regarding Titan material properties. Overall, observations of Titan point to a world pervasively influenced by fluvial processes, for which appropriate terrestrial analogs and formulations may provide insight.

An experimental study on turbulence modification in the near-wall boundary layer of a dilute gas-particle channel flow

Turbulence modifications of a dilute gas-particle flow are experimentally investigated in the lower boundary layer of a horizontal channel by means of a simultaneous two-phase PIV measurement technique. The measurements are conducted in the near-wall region with y + < 250 at Re τ (based on the wall friction velocity u τ and half channel height h) = 430. High spatial resolution and small interrogation window are used to minimize the PIV measurement uncertainty due to the velocity gradient near the wall. Polythene beads with the diameter of 60 μm (d + = 1.71, normalized by the fluid kinematic viscosity ν and u τ) are used as dispersed phase, and three low mass loading ratios (Φ m ) ranging from 10−4 to 10−3 are tested. It is found that the addition of the particles noticeably modifies the mean velocity and turbulent intensities of the gas-phase, as well as the turbulence coherent structures, even at Φ m = 0.025 %. Particle inertia changes the viscous sublayer of the gas turbulence with a smaller thickness and a larger streamwise velocity gradient, which increases the peak value of the streamwise fluctuation velocity ( $$ u_{\text{rms}}^{ + } $$ ) of the gas-phase with its location shifting to the wall. Particle sedimentation increases the roughness of the bottom wall, which significantly increases the wall-normal fluctuation velocity ( $$ v_{\text{rms}}^{ + } $$ ) and Reynolds shear stress ( $$ - \langle u^{ \prime } v^{\prime } \rangle^{ + } $$ ) of the gas-phase in the inner region of the boundary layer (y + < 10). Under effect of particle–wall collision, the Q2 events (ejections) of the gas-phase are slightly increased by particles, while the Q4 events (sweeps) are obviously decreased. The spatial scale of the coherent structures near the wall shrinks remarkably with the presence of the particles, which may be attributed to the intensified crossing-trajectory effects due to particle saltation near the bottom wall. Meanwhile, the $$ v_{\text{rms}}^{ + } $$ and $$ - \langle u^{ \prime } v^{\prime } \rangle^{ + } $$ of the gas-phase are significantly reduced in the outer region of the boundary layer (y + > 20).