Wake Length Research Articles

Large eddy simulation of flow and heat transfer in a channel with a detached rib array

Ribbed channels are widely used to enhance heat transfer in various heat exchange equipment. However, the heat transfer is locally deteriorated immediately behind the rib due to the flow separation. To overcome this shortcoming, a detached rib array has been proposed recently. In the present study, large eddy simulations (LES) of turbulent flow and heat transfer in a channel with a detached rib array have been conducted. The no-slip and no-jump conditions on the rib surface are satisfied in the Cartesian coordinates by using an immersed boundary method. Experiments are conducted as well to validate the simulation. The velocity and temperature fields are obtained by a hot wire and a thermocouple, respectively. The surface heat transfer is measured using the thermochromic liquid crystal with a high spatial resolution. Compared with the attached rib, the detached one enhances the heat transfer underneath the rib, whereas the channel wall downstream of the rib shows lower heat transfer rate. By investigating the effect of the clearance between the rib and the wall, we have found an intermediate flow pattern, where the counter-rotating vortex pair and the separation bubble coexist. Including the new flow pattern, we discuss the flow characteristics such as the wake length and the locus of the saddle points, and the flow physics behind the local heat transfer distribution on the channel wall based on the instantaneous flow and thermal fields. The turbulence data near the solid surface are also presented, which have not been provided by previous experiments.

Numerical study of the effect of plastic wake on plasticity‐induced fatigue crack closure

ABSTRACTFatigue crack closure is strongly influenced by the plastic wake developed because of the action of precedent cycles. It is related to the load sequence and is an additional difficulty for its determination. Finite‐element method has been an alternative for the study of crack closure, commonly in constant‐amplitude loading. However, such analyses are complex and computationally expensive, the length of the wake simulated being a critical parameter. In this paper, a comprehensive study of the effect of the plastic wake in fatigue crack closure is made. It is structured in two parts: one regarding the correct numerical modelling process and the other focussed on the influence of the wake under moderate variable‐amplitude loading. After a brief description of the numerical methodology, results for different wake lengths are reported. The plastic wake is modelled with a new approach in which the final crack tip is fixed. Information regarding potential error is provided. Second, the load sequence effect is discussed. Crack closure is obtained for several load ratios, with wakes developed with different stress ratios. This permits the analysis of the influence of the load sequence over the crack‐driving force compared with constant‐amplitude loading.

비선형 와류격자법을 이용한 낮은 종횡비 날개의 공력특성 계산

본 논문에서는 새로운 비선형 와류격자법 계산 과정이 제안된다. 기존의 계산 과정은 자유와의 형태 계산을 위해 내부 반복계산 및 하향이완법을 포함한다. 하지만 본 논문에서는 유사 정상 개념에 기초한 새로운 수식을 제안하여 자유와의 형태를 계산함으로써, 계산 과정에서 내부 반복계산 및 하향이완법을 생략한다. 또한 반복계산이 진행됨에 따라 각 분절에 유도되는 유속도를 적절히 평균해 줌으로써 알고리듬의 수치적 안정성을 향상시킨다. 그리고 낮은 종횡비 날개에 대한 수치실험을 수행하여 분절의 길이, 와류중심반경, 후류영역 계산범위 등과 같은 중요 인자들의 적절한 기준을 경험적으로 결정한다. new computational procedure for the Non-Linear Vortex Lattice Method (NLVLM) is suggested in this work. Conventional procedures suggested so far usually involves inner iteration loop to update free vortex shape and an under-relaxation based iteration loop to determine the free vortex shape. In this present work, we suggest a new formula based on quasi-steady concept to fix free vortex shape which eliminates the need for inner iteration loop. Further, the ensemble averaging of the induced velocities for a given free vortex segment evaluated at each iteration significantly improves the convergence property of the algorithm without resorting to the under-relaxation technique. Numerical experiments over several low aspect ratio wings are carried out to obtain optimal empirical parameters such as the length of the free vortex segment, the vortex core radius, and the rolled-up wake length.

The self-similar rise of a buoyant thermal in very viscous flow

An exact similarity solution is obtained for the rise of a buoyant thermal in Stokes flow, in which both the rise height and the diffusive growth scale like t1/2 as time t increases. The dimensionless problem depends on a single parameter Ra = B/(νκ) – a Rayleigh number – based on the (conserved) total buoyancy B of the thermal, and the kinematic viscosity ν and thermal diffusivity κ of the fluid. Numerical solutions are found for a range of Ra. For small Ra there are only slight deformations to a spherically symmetric Gaussian temperature distribution. For large Ra, the temperature distribution becomes elongated vertically, with a long wake containing most of the buoyancy left behind the head. Passive tracers, however, are advected into a toroidal structure in the head. A simple asymptotic model for the large-Ra behaviour is obtained using slender-body theory. The width of the thermal is found to increase like (κt)1/2, while the wake length and rise height both increase like (RalnRa)1/2(κt)1/2, consistent with the numerical results. Previous experiments suggest that there is a significant transient regime.

Vortex-induced vibrations of a circular cylinder in laminar and turbulent flows

Abstract Experimental results on the behaviour of a freely vibrating circular cylinder in laminar and turbulent flows are presented. Wind tunnel tests have been performed by varying the cylinder roughness and the mass-damping parameter, m * ζ . The effects of surface roughness and flow turbulence have been considered in term of an effective Reynolds number, Re eff . In this way, it has been possible to test the sample before and after the beginning of the cylinder boundary layer transition. It has been evidenced that m * ζ is not the sole parameter influencing the response during lock-in; Reynolds number also plays an important role. If m * ζ is fixed, the responses decrease as Re eff increases. Moreover, it has been observed that the cylinder may experience vortex-induced vibrations even in the critical Re eff regime characterized by a cessation of coherent vortex shedding in steady configuration. The effects of m * ζ and Re eff on the critical velocity (the velocity at which the maximum amplitude of response is approached), on the wideness of the lock-in range, and on the wake correlation length are also discussed.

Turbulence Model Assessment for Flow Across a Row of Confined Cylinders

The effectiveness of five different turbulence models is assessed for the flow across a row of confined cylinders at a pitch-to-diameter ratio of 1.7 and at Reynolds numbers ranging from 2621 to 55 920. Models examined include the one-equation Spalart-Almaras model; two-equation realizable k - ɛ, k - ω, and shear stress transport models; and a four-equation v2 - f model. Quantities compared against published experimental data include minor loss coefficients, separation angles about cylinders, wake lengths behind cylinders, and streamwise velocity profiles at the periodic inlet/outlet boundaries. Results indicate that each of the models did a reasonable job in predicting the minor loss coefficient as a function of Reynolds number. With the exception of the k - ɛ model, each was also able to predict the experimentally observed trend of decreasing wake and separation lengths with increasing Reynolds number. In addition, all models also predicted a local minimum in the separation angle about the inner cylinder as a function of Reynolds number, which has also been observed experimentally. Our conclusion is that the v2 - f model performed slightly better at predicting the experimental data than any of the other models examined, although at the computational expense of solving two additional equations.

Microscale Fracture Toughness Testing of TiAl PST Crystals

AbstractA microscale fracture testing technique has been applied to examine the fracture properties of lamellar in TiAl PST crystals. Micro-sized cantilever specimens with a size ˜ 10×20×50 μm3 were prepared from Ti-48Al two-phase single crystals (PST) lamellar by focused ion beam (FIB) machining. Notches with a width of 0.5 μm and a depth of 5 μm were also introduced into the specimens by FIB. Two types of notch directions (interlamellar and translamellar) were selected when introducing the notches. Fracture tests were successfully completed using a mechanical testing machine for micro-sized specimens at room temperature. The fracture toughness (KQ) values of the interlamellar type specimens were obtained in the range 1.5–3.6 MPam1/2, while those of the translamellar specimens were 5.0–8.1 MPam1/2. These fracture toughness values are lower than those having been previously reported in conventional TiAl PST samples. For macro-sized specimens, extrinsic toughening mechanisms, including shear ligament bridging, act in the crack wake, and the crack growth resistance increases rapidly with increasing length of crack wake for lamellar structured TiAl alloys. In contrast, the crack length in microsized specimens is only 2–3 μm. This indicates that extrinsic toughening mechanisms are not activated in micro-sized specimens. This also indicates that intrinsic fracture toughness can be evaluated using microscale fracture toughness testing.

Interaction between Taylor bubbles rising in stagnant non-Newtonian fluids

The interaction between Taylor bubbles rising in stagnant non-Newtonian solutions was studied. Aqueous solutions of carboxymethylcellulose (CMC) and polyacrylamide (PAA) polymers were used to study the effect of different rheological properties: shear viscosity and viscoelasticity. The solutions studied covered a range of Reynolds numbers between 10 and 714, and Deborah numbers up to 14. The study was performed with pairs of Taylor bubbles rising in a vertical column (0.032 m internal diameter) filled with stagnant liquid. The velocities of the leading and trailing bubbles were measured by sets of laser diodes/photocells placed along the column. The velocity of the trailing bubble was analysed together with the liquid velocity profile in the wake of a single rising bubble (Particle Image Velocimetry data obtained from the literature). For the less concentrated CMC solutions, with moderate shear viscosity and low viscoelasticity, the interaction between Taylor bubbles was similar to that found in Newtonian fluids. For the most concentrated CMC solution, which has high shear viscosity and moderate viscoelasticity, a negative wake forms behind the Taylor bubbles, inhibiting coalescence since the bubbles maintain a minimum distance of about 1 D between them. For the PAA solutions, with moderate shear viscosity but higher viscoelasticity than the CMC solutions, longer wake lengths are seen, which are responsible for trailing bubble acceleration at greater distances from the leading bubble. Also in the PAA solutions, the long time needed for the fluid to recover its initial shear viscosity after the passage of the first bubble makes the fluid less resistant to the trailing bubble flow. Hence, the trailing bubble can travel at a higher velocity than the leading bubble, even at distances above 90 D.

Steady flow across a confined square cylinder: Effects of power-law index and blockage ratio

The effect of blockage ratio on the flow characteristics of power-law fluids across a square cylinder confined in a channel has been investigated for the range of conditions 1 ≤ Re ≤ 45, 0.5 ≤ n ≤ 2.0 and β = 1/8, 1/6 and 1/4. Extensive numerical results on the individual and total drag coefficients, wake length, stream function, vorticity and power-law viscosity on the surface of the square cylinder are reported to determine the combined effects of the flow behavior index, blockage ratio and Reynolds number. The size of the wake region is influenced more by blockage than by power-law index. Similarly, drag is also seen to be more influenced by blockage ratio and the Reynolds number than that by the power-law index.

The effects of axis ratio on laminar fluid flow around an elliptical cylinder

An elliptical cylinder is a generic shape which represents a flat plate at its minor to major axis ratio (AR) limits of zero and infinity, and a circular cylinder at AR of unity. While incompressible flows over a streamwise flat plate (AR = 0), a cross-stream flat plate (AR = ∞), and a circular cylinder have been studied extensively, the role of AR on the detailed flow structure is still not well understood. Therefore, a numerical study was conducted to examine the flow field around an elliptical cylinder over a range of ARs from 0.3 to 1, with the major axis parallel to the free-stream, at a Reynolds number of 40 based on the hydraulic diameter. The control volume approach of FLUENT was used to solve the fluid flow equations, assuming the flow over the cylinder is unbounded, steady, incompressible and two-dimensional. It has been found that a pair of steady vortices forms when AR reaches a critical value of 0.34; below this value no vortices are formed behind the elliptical cylinder. Various wake parameters, drag coefficient, pressure and velocity distributions, have been characterized as functions of AR. The wake size and the drag coefficient are found to increase with the increase of AR. Quadratic correlations have been obtained to describe the relations of wake length and drag coefficient with axis ratio.

Stepovers that migrate with respect to affected deposits: field characteristics and speculation on some details of their evolution

Abstract Traditionally, geologists have viewed strike-slip stepover regions as progressively increasing in structural relief with increasing slip along the principal displacement zones (PDZs). In contrast, some stepover regions may migrate along the strike of the PDZs with respect to deposits affected by them, leaving a ‘wake’ of formerly affected deposits trailing the active stepover region. Such stepovers generate comparatively little structural relief at any given location. For restraining bends of this type, little exhumation and erosion takes place at any given location. Another characteristic of migrating stepovers is local tectonic inversion that may migrate along the strike of the PDZs. This is most easily observed for migrating releasing bends where the wake is composed of former pull-apart basin deposits that have been subject to shortening and uplift. This type of basin inversion occurs along the San Andreas Fault, wherein the wake is affected by regional transpression. Some migrating stepovers may evolve by propagation of the PDZ on one side of the stepover, and shut-off of the PDZ on the other side. Possible examples of migrating stepovers are present along the northern San Andreas fault system at scales from metres (sag ponds and pressure ridges) to tens of kilometres (large basins and transpressional uplifts). Migrating stepovers and ‘traditional’ stepovers may be end members of stepover evolutionary types, and the ratio of wake length to the amount of slip along the PDZs during stepover development measures the ‘migrating stepover component’ of a given stepover. For a ‘pure’ migrating type, the wake length may be equal to or greater than the PDZ cumulative slip during the time of stepover evolution, whereas for a ‘pure’ traditional type, there would be no wake.

Flow patterns in the wake of a Taylor bubble rising through vertical columns of stagnant and flowing Newtonian liquids: An experimental study

The flow in the wake and near-wake regions of individual Taylor bubbles rising through stagnant and co-current vertical columns of Newtonian liquids was studied, employing simultaneously particle image velocimetry (PIV) and pulsed shadowgraphy techniques (PST). Experiments were made with water and aqueous glycerol solutions covering a wide range of viscosities ( 1 × 10 - 3 Pa s < μ < 1.5 Pa s ) , in an acrylic column of 32 mm ID. Different wake structures (laminar, transitional and turbulent) are identified, in both stagnant and co-current flow conditions. In stagnant liquids, the wake flow pattern is only dependent on the dimensionless group N f . The different types of wakes obtained are in accordance with the critical N f numbers proposed in previous works. For co-current flow conditions, the flow patterns in the wake depend on the Reynolds number based on the relative (to the bubble) average velocity of the upward liquid flow, the laminar-transitional and transitional-turbulent limits being for the first time experimentally determined. The wake flow patterns are quantified by means of instantaneous and average flow fields. Values for the wake length and wake volume are also presented and compare well with correlations found in literature. Study of the flow in the near-wake zone enabled determination of the distance needed to recover the undisturbed liquid velocity profile. The detailed study of the flow in the wake and near-wake regions is an important contribution to better understanding the interaction and coalescence mechanisms between Taylor bubbles. The data reported are relevant to the validation of numerical simulation codes in the vertical slug flow regime.

Steady Flow of Power-law Fluids Across a Square Cylinder

The two-dimensional flow of power-law fluids over an isolated unconfined square cylinder has been investigated numerically in the range of conditions 1 ≤ Re ≤ 45 and 0.5 ≤ n ≤ 2.0. The global quantities such as wake length, drag coefficients and the detailed kinematic variables like stream function, vorticity and so on, have been calculated for the above range of conditions. In particular, the effects of Reynolds number and of the power-law index have been investigated in the steady flow regime. The shear-thinning fluid behaviour increases the drag above its Newtonian value whereas the shear-thickening behaviour reduces the drag below its Newtonian value. However, as the value of the Reynolds number is gradually increased, the role of power-law index diminishes. Similarly, the wake size is shorter in shear-thinning fluids than that in Newtonian fluids under otherwise indentical conditions.

Hydrodynamics of model Posidonia oceanica patches in shallow water

The hydrodynamics of simulated patches of the Mediterranean seagrass Posidonia oceanica were studied in laboratory flume experiments in which the height of the pronated canopy was always greater than half the total water depth. The effects of variations in speed (from 0.08 m s 21 to 0.24 m s 21 ) and patch configuration on the hydrodynamics were investigated. Significant speeds penetrated the patches to approximately half their height. Reducing speed did not change the flow patterns observed, except to weaken and blur them. Flow encountering a single patch formed a turbulent wake at the height of the top of the canopy. Within this wake, the vertical shear stress decreased monotonically downstream, but the Reynolds stress increased initially and then decayed. When a second patch was positioned within the region where Reynolds stress increased (referred to as the ‘‘06 patch’’), the wake center penetrated it, causing average turbulent velocities with horizontal components 3.3 times higher and vertical components 4.2 times higher than in the upstream patch. When this patch was positioned where the Reynolds stress decayed (referred to as the ‘‘14 patch’’), the wake center rose above it. Nevertheless, the turbulence in the 14 patch had horizontal components 12% higher and vertical components 22% higher on average than in the 06 patch because its upstream end was closer to the Reynolds stress maximum. Thus the ratio of the patch separation to the length of wake in which the Reynolds stress increased was identified as central to quantifying the turbulence within the downstream patch. The increased turbulence is likely to be important in determining sedimentary and ecological patch characteristics by increasing retention of particulates in suspension and thus reducing depositional rates of, for example, larvae, nutrients, and dead organic matter.

Flow and deformation of the capillary glycocalyx in the wake of a leukocyte

An analysis is presented of the axisymmetric axial and radial flow and deformation fields throughout the endothelial-cell glycocalyx surface layer in the wake region behind a leukocyte moving steadily through a capillary. The glycocalyx, modeled as a thin poroelastic surface layer lining the capillary wall, is assumed to consist of a binary mixture of a linearly viscous fluid constituent and an isotropic, highly compressible, linearly elastic solid constituent having a vanishingly small solid-volume fraction. Invoking the asymptotic approximations of lubrication theory in a frame of reference translating with the leukocyte, closed-form solutions are obtained to the leading-order boundary-value problems governing the axial and radial flow and deformation fields throughout the glycocalyx as well as the axial and radial flow fields throughout the free capillary lumen within the wake. A simple asymptotic expression is obtained for the length lchar of the wake region in terms of the translational speed U0 of the leukocyte, and the equilibrium thickness h0, permeability k0, and aggregate elastic modulus HA of the glycocalyx. The predicted wake length, as seen from an observer moving in a reference frame attached to the leukocyte, is consistent with the recovery time predicted from a one-dimensional analysis of glycocalyx deformation through a quiescent inviscid fluid. The two-dimensional fluid dynamical analysis presented here thus provides the appropriate relationships for extracting estimates of the mechanoelectrochemical properties of the glycocalyx from physiologically realistic constitutive models developed under simplified one-dimensional flow regimes. The directly measurable quantities lchar,U0, and h0, which are obtainable from in vivo observations of the wake region behind a leukocyte moving steadily through a capillary, can therefore be connected, through the results of this analysis, to estimates of the mechanoelectrochemical properties of the glycocalyx on vascular endothelial cells.

Steady non?Newtonian flow past a circular cylinder: a numerical study

The steady and incompressible flow of non-Newtonian fluids past a circular cylinder is investigated for power law indices n between 0.2 and 1.4, blockage ratios of 0.037, 0.082 and 0.164, and the Reynolds numbers Re of 1, 20 and 40, using a stream function/vorticity formulation. The governing field equations have been solved by using a second-order accurate finite difference method to determine the drag coefficient, wake length, separation angle and flow patterns, and to investigate their dependence on power law index, blockage ratio and Reynolds number. The results reported here provide fundamental knowledge on the dependence of engineering flow parameters on blockage ratio and power law index, and further show that the effects on stream line and iso-vorticity patterns which result from an increase in the blockage ratio are similar to those which result from a decrease in the power law index.

Planar flow past two or more blades in ground effect

Planar flow past a finite number of thin blades travelling in sequence, aligned or nearly aligned over flat ground, is examined analytically and numerically for large Reynolds numbers. The work is motivated by concerns with rotorcraft in ground effect. The representative blade length, wake length and height above ground are taken to be comparable, with each wake (except the final one) intersecting the next blade. Inner-outer interaction covers the whole system as all the wake shapes adjust to maintain pressure equality, forcing viscous-inviscid coupling through lateral offsets within each wake. Results are presented for several configurations, in the frame of the blades with the ground moving at freestream speed. The limits of small relative height and of many blades are then investigated. It is found, for the case of identical blade and wake lengths. that as the height is reduced the ground effect first becomes significant at heights just below one half of the blade length but then grows substantially; and that a virtually streamwise periodic motion ernerges for about three or more blades.

Numerical Study of Steady Flow Past a Sphere in an Aligned Magnetic Field

AbstractThe flow of a steady, incompressible, viscous, electrically conducting fluid past a sphere in the presence of uniform magnetic field parallel to the undisturbed flow is investigated using the finite difference method. The multigrid method with a defect correction (DC) technique is used to achieve the second order accurate solution. The Hartmann number M is used as the perturbation parameter. It has been found that the increase of magnetic field decreases the wake length (L) and increases the drag coefficient. The graphs of streamlines, vorticity lines, drag coefficient, wake length, surface pressure and surface vorticity are presented and discussed

Far-Field Simulation of the Hawaiian Wake: Sea Surface Temperature and Orographic Effects*

Recent satellite observations reveal far-reaching effects of the Hawaiian Islands on surface wind, cloud, ocean current, and sea surface temperature (SST) that extend leeward over an unusually long distance (.1000 km). A three-dimensional regional atmospheric model with full physics is used to investigate the cause of this long wake. While previous wind‐wake studies tend to focus on regions near the islands, the emphasis here is the far-field effects of SST and orography well away from the Hawaiian Islands. In response to an island-induced SST pattern, the model produces surface wind and cloud anomaly patterns that resemble those observed by satellites. In particular, anomalous surface winds are found to converge onto a zonal band of warmer water, with cloud liquid water content enhanced over it but reduced on the northern and southern sides. In the vertical, a two-cell meridional circulation develops of a baroclinic structure with the rising motion and thicker clouds over the warm water band. The model response in the wind and cloud fields supports the hypothesis that ocean‐ atmosphere interaction is crucial for sustaining the island effects over a few thousand kilometers. Near Hawaii, mountains generate separate wind wakes in the model lee of individual islands as observed by satellites. Under orographic forcing, the model simulates the windward cloud line and the southwest-tilted cloud band leeward of the Big Island. In the far field, orographically induced wind perturbations are found to be in geostrophic balance with pressure anomalies, indicative of quasigeostrophic Rossby wave propagation. A shallowwater model is developed for disturbances trapped in the inversion-capped planetary boundary layer. The westward propagation of Rossby waves is found to increase the wake length significantly, consistent with the threedimensional simulation.

Experimental investigations and numerical simulations for an open channel flow of a weak elastic polymer solution around a T-profile

The present paper is concerned with experimental and numerical investigations of planar complex flows of "weak" elastic polymer solutions (whose concentration are below the critical overlap concentration), characterised by small relaxation times (lambda<0.1 s) and almost constant shear viscosities for small and medium shear rates. The main aim of the study is to detect to what extent a very small amount of elasticity present in a viscous fluid can influence its behaviour in complex flows, without introducing major modifications of classical rheological tests. The samples are polymer solutions of low PIB molecular weight dissolved in highly viscous Newtonian mineral oil. The analysed motion is steady, and takes place in an open channel around a "T" profile. Maximum values of the characteristic parameters for the experiments, the Reynolds and Weissenberg numbers, were 45 and 0.1, respectively. The experiments show a decrease of the wake length downstream the profile for weak elastic solutions in comparison to the Newtonian solvent. Actually, the same wake length as in the Newtonian case was obtained for tested polymer solutions, but at higher Re numbers. Numerical simulations using the Giesekus model predict the same behaviour and are consistent with experiments from both qualitative and quantitative point of views. The results of research conclude that, even in small amounts, the presence of elasticity in pure viscous liquids induces quantitative changes from Newtonian flow in complex dominant elongational flows, at elongational rates for which the sudden thickening of extensional viscosity is remarkable. The study is important, since it should enable better understanding and modelling of viscoelastic flows that involve dilute polymer solutions, or fluids with similar rheology; biofluid mechanics being one area of application of this research. Corroboration of experimental flow visualization with numerical simulation is currently a feasible method used to characterise weak elastic polymer solutions, since classical rheological techniques generally fail to obtain realistic values of relaxation time for these particular viscoelastic fluids.