Streamwise Rib Research Articles

Low-Velocity Zone in Smooth Pipe Culvert with and without Streamwise Rib for Fish Passage

AbstractUnimpeded waterway connectivity is a requirement for all freshwater fish. While box culverts are considered the most effective design in terms of upstream fish passage, circular culverts ar...

Hydrodynamics and secondary currents in an asymmetrical rectangular canal with streamwise beam

While the literature on transverse beams in open channels is broad, there is comparatively less understanding of the hydrodynamics of channels with streamwise ribs. In the current study, an asymmetrical canal with a sidewall longitudinal beam was studied experimentally to gain some fundamental understanding of the implications in terms of turbulence and environmental applications. The sidewall beam induced regular losses along the canal, with a complicated velocity field and secondary currents. The data showed a contrasted longitudinal velocity map, with high and low velocity zones. The lowest velocities were typically recorded underneath the sidewall beam. Complicated secondary currents of Prandtl’s second kind developed in the inner and outer corners of the beams, as well as in the square cavity underneath.

Numerical investigation of high pressure turbine blade tip-shaping effects on the aerothermal and dynamic performance

Purpose In order to improve the engine reliability and efficiency, an effective way is to reform the turbine blade tip conformation. The paper aims to discuss this issue. Design/methodology/approach The present research provides several novel tip-shaping structures, which are considered to control the blade tip loss. Four different tip geometries have been studied: flat tip, squealer tip, flat tip with streamwise ribs and squealer tip with streamwise ribs. The tip heat transfer and leakage flow are both analyzed in detail, for example the tip heat transfer coefficient, tip flow and local pressure distributions. Findings The results show that the squealer seal and streamwise rib can reduce the tip heat transfer and leakage loss, especially for the squealer tip with streamwise ribs. The tip and near-tip flow patterns at the different locations of axial chord reflect that both the squealer seal and streamwise rib structure can control the tip leakage flow loss. In addition, the analysis of the aerodynamic parameters (the static pressure and turbine efficiency) also indicates that the squealer tip with streamwise ribs obtains the highest adiabatic efficiency with an increase of 2.34 percent, compared with that of the flat tip case. Originality/value The analysis of aerothermal and dynamic performance can provide a reference for the blade tip design and treatment.

Self-sustaining turbulent wake characteristics in fluid–structure interaction of a square cylinder

We present a numerical study on the fluid–structure interaction of a square cylinder at subcritical Reynolds numbers 1400≤Re≤10,000. Variation in spatial and temporal structures during the self-sustaining regeneration cycle are investigated via a three-dimensional Navier–Stokes flow coupled with a freely vibrating square cylinder at relatively low mass ratio. We employ a variational fluid–structure interaction formulation based on the recently developed partitioned iterative scheme and the dynamic subgrid-scale turbulence model. To begin, we assess the response amplitudes, the synchronization regimes and the vortex shedding patterns against the experimental measurements for the flow-induced vibration of a square cylinder at zero incidence angle. Of particular interest is to predict and analyze the synchronization regimes and the associated wake structures for a range of reduced velocity. The vibration of the cylinder provides an avenue for the merging of smaller eddies in the vicinity of the cylinder and there are relatively more clustered spanwise rollers and streamwise ribs as compared to the stationary counterpart. We provide a comparative assessment of Reynolds stress distributions in the near-wake region between the VIV lock-in case and its stationary counterpart. We find that the spatial symmetry of the shearing process in the wake shifts to the temporal symmetry of Reynolds stress when the cylinder is free to vibrate. Consequently, in the vibrating case, the competition between the mean shear growth and damping results in a relatively lower frequency shearing as compared to the stationary cylinder. We introduce a representative control volume in the near-wake region to assess the kinetic energy and enstrophy evolution for the stationary and vibrating configurations. We examine the core reason of the matching of periodic wake frequency with the vibrating cylinder frequency through the development of near-wake flow structures and the kinetic energy evolution. By combining these results with the self-sustained process of coherent vortex structure development, we finally explain the formation of intermediate hairpin-like structures in close proximity to the vibrating cylinder and the absence of them in the stationary cylinder.

Numerical investigation of heat transfer and fluid flow in a rotating rectangular channel with variously-shaped discrete ribs

A numerical study is performed to investigate the effects of various discrete rib configurations on the heat transfer and fluid flow characteristics of a rotating rectangular straight channel (aspect ratio of 2:1) with 45° orientation. Three parameters of the discrete rib configuration - rib streamwise distance, rib widthwise distance, and inner-half-rib angle - are examined based on a continuous inclined rib. The blockage ratio (e/Dh) is 0.1 and the pitch ratio (P/e) is 10. The Reynolds number is fixed at 10,000 in each case, while the rotation number is varied from 0 to 0.7. Details of the turbulent flow structure, turbulence kinetic energies, temperature fields, normalized Nusselt numbers, friction penalties and thermal performance factors were obtained by Computation of Fluid Dynamics (CFD) with the k-ω SST turbulence model. The results show that a small streamwise rib gap can effectively enhance the leading wall heat transfer. The heat transfer decreases gradually as the streamwise rib gap is enlarged. The inner-half-rib angle β provides the most conspicuous effects on heat transfer and friction loss, and the best heat transfer appears at β = 60° or 75° for different rotating conditions. The case with a rib streamwise gap normalized distance of 0.2 and inner-half-rib angle of 45° provides best thermal performance. A widthwise rib gap is favorable in reducing pressure drop, but its heat transfer augmentation is limited.

Characteristics of distinct flow regimes in the wake of an infinite span normal thin flat plate

The wake of an infinite, two-dimensional (2D), thin flat plate of height h was studied using Direct Numerical Simulation (DNS) for two Reynolds numbers, Re=1.2×103 and 2.4 × 103. The vortex shedding Strouhal number was 0.158. In addition to the high - and low - intensity shedding regimes (H and L) first reported by Najjar and Balachandar (1998), a distinct period of reorganization (M) is identified following regime H. The average flow characteristics for regime M are similar to those of the long-term mean flow. The regime-averaged recirculation length at Re=1.2×103 was 2.16h during H, 3.60h during L and 2.81h during M. Whereas the spanwise vortex rollers are well-organized during both regimes H and M, the arrangement of the streamwise ribs is much more regular and can be observed further downstream in regime H than M. The flow is highly three-dimensional during regime L, which includes less-coherent vortex rollers and spanwise randomly distributed ribs. The impact of this behavior on the roll-up, and thus the extension of the shear layer, is identified as a driving mechanism for generation and sustainability of the periodic wake behavior.

Optimal perturbations in time-dependent variable-density Kelvin–Helmholtz billows

We analyse the influence of the specific features of time-dependent variable-density Kelvin–Helmholtz (VDKH) roll-ups on the development of three-dimensional secondary instabilities. Due to inertial (high Froude number) baroclinic sources of spanwise vorticity at high Atwood number (up to 0.5 here), temporally evolving mixing layers exhibit a layered structure associated with a strain field radically different from their homogeneous counterpart. We use a direct-adjoint non-modal linear approach to determine the fastest growing perturbations over a single period of the time-evolving two-dimensional base flow during a given time interval $[t_{0},T]$. When perturbations are seeded at the initial time of the primary KH mode growth, i.e. $t_{0}=0$, it is found that additional mechanisms of energy growth are onset around a bifurcation time $t_{b}$, a little before the saturation of the primary two-dimensional instability. The evolution of optimal perturbations is thus observed to develop in two distinct stages. Whatever the Atwood number, the first period $[t_{0},t_{b}]$ is characterised by a unique route for optimal energy growth resulting from a combination of the Orr and lift-up transient mechanisms. In the second period $[t_{b},T]$, the growing influence of mass inhomogeneities raises the energy gain over the whole range of spanwise wavenumbers. As the Atwood number increases, the short spanwise wavelength perturbations tend to benefit more from the onset of variable-density effects than large wavelength ones. The extra energy gain due to increasing Atwood numbers relies on contributions from spanwise baroclinic sources. The resulting vorticity field is structured into two elongated dipoles localised along the braid on either side of the saddle point. In return they yield two longitudinal velocity streaks of opposite sign which account for most of the energy growth. This transition towards three-dimensional motions is in marked contrast with the classic streamwise rib vortices, so far accepted as the paradigm for the transition of free shear flows, either homogeneous or not. It is argued that the emergence of these longitudinal velocity streaks is generic of the transition in variable-density shear flows. Among them, the light round jet is known to display striking side ejections as a result of the loss of axisymmetry. The present analysis helps to renew the question of the underlying flow structure behind side jets, otherwise based on radial induction between pairs of counter-rotating longitudinal vortices (Monkewitz & Pfizenmaier, Phys. Fluids A, vol. 3 (5), 1991, pp. 1356–1361). Instead, it is more likely that side ejections would result from the convergence of the longitudinal velocity streaks near the braid saddle point. When the injection time is delayed so as to suppress the initial stage of energy growth, a new class of perturbations arises at low wavenumber with energy gains far larger than those observed so far. They correspond to the two-dimensional Kelvin–Helmholtz secondary instability of the baroclinically enhanced vorticity braid discovered by Reinaud et al. (Phys. Fluids, vol. 12 (10), pp. 2489–2505), leading potentially to another route to turbulence through a two-dimensional fractal cascade.

Apparent Temperature Jump and Thermal Transport in Channels With Streamwise Rib and Cavity Featured Superhydrophobic Walls at Constant Heat Flux

This paper presents an analytical investigation of constant property, steady, fully developed, laminar thermal transport in a parallel-plate channel comprised of metal superhydrophobic (SH) walls. The superhydrophobic walls considered here exhibit microribs and cavities aligned in the streamwise direction. The cavities are assumed to be nonwetting and contain air, such that the Cassie–Baxter state is the interfacial state considered. The scenario considered is that of constant heat flux through the rib surfaces with negligible thermal transport through the air cavity interface. Closed form solutions for the local Nusselt number and local wall temperature are presented and are in the form of infinite series expansions. The analysis show the relative size of the cavity regions compared to the total rib and cavity width (cavity fraction) exercises significant influence on the aggregate thermal transport behavior. Further, the relative size of the rib and cavity module width compared to the channel hydraulic diameter (relative module width) also influences the Nusselt number. The spatially varying Nusselt number and wall temperature are presented as a function of the cavity fraction and the relative module width over the ranges 0–0.99 and 0.01–1.0, respectively. From these results, the rib/cavity module averaged Nusselt number was determined as a function of the governing parameters. The results reveal that increases in either the cavity fraction or relative module width lead to decreases in the average Nusselt number and results are presented over a wide range of conditions from which the average Nusselt number can be determined for heat transfer analysis. Further, analogous to the hydrodynamic slip length, a temperature jump length describing the apparent temperature jump at the wall is determined in terms of the cavity fraction. Remarkably, it is nearly identical to the hydrodynamic slip length for the scenario considered here and allows straightforward determination of the average Nusselt number for any cavity fraction and relative rib/cavity module width.

Developing and fully developed turbulent flow in ribbed channels

Wall-mounted roughness features, such as ribs, are often placed along the walls of a channel to increase the convective surface area and to augment heat transfer and mixing by increasing turbulence. Depending on the relative roughness size and orientation, the ribs also have varying degrees of increased pressure losses. Designs that use ribs to promote heat transfer encompass the full range of having only a few streamwise ribs, which do not allow fully developed flow conditions, to multiple streamwise ribs, which do allow the flow to become fully developed. The majority of previous studies have focused on perturbing the geometry of the rib with little attention to the spatially and temporally varying flow characteristics and their dependence on the Reynolds number. A staggered rib-roughened channel study was performed using time-resolved digital particle image velocimetry (TRDPIV). Both the developing (entry region) and a fully developed region were interrogated for three Reynolds numbers of 2,500, 10,000, and 20,000. The results indicate that the flow was more sensitive to Reynolds number at the inlet than within the fully developed region. Despite having a similar mean-averaged flowfield structure over the full Reynolds number range investigated, the population and distribution of coherent structures and turbulent dissipation within the fully developed region were also found to be Reynolds number dependent. Exploring the time-accurate flow characteristics revealed that in addition to vortices shed from the rib shear layer, the region of the rib wake was governed by a periodic process of bursting of the wake vortices resulting in the intermittent ejection of the inter-rib recirculation region into the core flow. This periodic process was the driving mechanism resulting in mixing and heat transfer augmentation. A quadrant-splitting burst analysis was also performed to determine the characteristic frequency and duration of inter-rib bursting as well as the wake shedding frequency, both of which were determined to be Reynolds number dependent.

Shape optimization of three-dimensional channel roughened by angled ribs with RANS analysis of turbulent heat transfer

A numerical procedure for optimizing the shape of three-dimensional channel with angled ribs extruded on both walls is presented to enhance turbulent heat transfer. The response surface based optimization is used as an optimization technique with Reynolds-averaged Navier–Stokes analysis of fluid flow and heat transfer. Shear stress transport (SST) turbulence model is used as a turbulence closure. Computational results for heat transfer rate show good agreements with experimental data. Four dimensionless variables such as, rib pitch-to-rib height ratio, rib height-to-channel height ratio, streamwise rib distance on opposite wall to rib height ratio, and the attack angle of the rib are chosen as design variables. The objective function is defined as a linear combination of heat transfer and friction loss related terms with a weighting factor. D-optimal method is used to determine the training points as a mean of design of experiment. Sensitivity of the objective function to each design variable has been evaluated. And, optimal values of the design variables have been obtained in a range of the weighting factor.

반응면 기법을 이용한 경사진 리브가 부착된 삼차원 열전달유로의 최적설계

A numerical optimization has been earned out to determine the shape of the three-dimensional channel With oblique ribs attached on both walls to enhance turbulent heat transfer. The response surface based optimization is used as an optimization technique with Reynolds-averaged Navier-Stokes analysis of fluid flow and heat transfer Shear stress transport (SST) turbulence model is used as a turbulence closure. Numerical results for heat transfer rate show good agreements With experimental data. Four dimensionless variables such as, rib pitch-to-rib height ratio, rib height-to-channel height ratio, streamwise rib distance on opposite wall to rib pitch ratio, and the attack angle of the rib are chosen as design variables The objective function is defined as a linear combination of heat-transfer and friction-loss related coefficients with a weighting factor. D-optimal method is used to determine the training points as a means of design of experiment Sensitivity of the objective parameters to each design variable has been analyzed And, optimal values of the design variables have been obtained in a range of the weighting factor.br/

난류열전달 향상을 위한 엇갈린 리브가 부착된 열전달면의 형상최적설계

This study presents a numerical procedure to optimize shape of streamwise periodic ribs mounted on both of the principal walls to enhance turbulent heat transfer in a rectangular channel flow. The response surface method is used as an optimization technique. The optimization is based on Navier-Stokes analysis of flow and heat transfer with k-εturbulence model. The width-to-height ratio of a rib, rib height-to-channel height ratio and rib pitch to rib height ratio are chosen as design variables. The object function is defined as a function of heat transfer coefficient and friction drag coefficient with weighting factor. Optimum shapes of the rib have been obtained for the range of 0.02 to 0.1 of weighting factor.

Reynolds averaged simulation of flow and heat transfer in ribbed ducts

The accuracy of modern eddy-viscosity type turbulence models in predicting turbulent flows and heat transfer in complex passages is investigated. The particular geometries of interest here are those related to turbine blade cooling systems. This paper presents numerical data from the calculation of the turbulent flow field and heat transfer in two-dimensional (2D) cavities and three-dimensional (3D) ribbed ducts. It is found that heat transfer predictions obtained using the v 2– f turbulence model for the 2D cavity are in good agreement with experimental data. However, there is only fair agreement with experimental data for the 3D ribbed duct. On the wall of the duct where ribs exist, predicted heat transfer agrees well with experimental data for all configurations (different streamwise rib spacing and the cavity depth) considered in this paper. But heat transfer predictions on the smooth-side wall do not concur with the experimental data. Evidence is provided that this is mainly due to the presence of strong secondary flow structures which might not be properly simulated with turbulence models based on eddy viscosity.

Numerical investigation of the scalar probability density function distribution in neutral and stably stratified mixing layers

Direct numerical simulations of a temporally-growing mixing layer are performed to examine how the resulting concentration probability density function (PDF) of an advected, nearly nondiffusive, passive scalar (numerical dye) varies under the combined effects of stable stratification, thermal conductivity, and perturbation of the initial velocity field. In stably-stratified mixing layers convective instabilities are responsible for the development of streamwise vortices or ribs. These exhibit shorter spanwise separation than in nonstratified shear layers and lead to differences in the subsequent three-dimensionalization of the flow field. Furthermore, vortex development is very efficiently suppressed by stratification in high-thermally-conducting fluids, because only small temperature gradients arise and thus negligible baroclinic vorticity reinforcement is available to counterbalance the stabilizing effects of buoyancy. This is reflected in smaller mixed-fluid total PDF areas with decreasing Prandtl number. The effect of coherent structures on the PDF distribution is seen to be significant. The main rolls are the cause of “global-concentration” mixing, i.e., mixing of fluid lumps with vastly different species concentration, reflected in nonmarching PDF peaks, where the peak of the PDF is located at a constant concentration value. Ribs, on the other hand, having shorter spatial extent and engendering mixing on a narrower concentration range, cause “local-concentration” mixing, which translates into marching PDF peaks. The combined action of the spanwise vortices rolling up, or pairing, and the ribs, may then give rise to tilted PDF distributions, which are intermediate between nonmarching and marching. The “pairing parameter,” used to predict the transition from nonmarching to marching PDFs, was found not to be reliable, small values being sufficient to allow the PDF to be marching in stratified flow. The scalar mean, and the scalar mean-mixed-fluid, concentrations are also investigated and are seen to deviate considerably from each other, depending on the strength and coherence of the vortical structures, the imposed stratification, and the thermal conductivity.

Vortical structure morphology in the initial region of a forced mixing layer: roll-up and pairing

Detailed three-dimensional phase-averaged measurements of the spanwise and streamwise vorticity formation and evolution in a forced mixing layer have been obtained. A plane two-stream mixing layer with a velocity ratio (U2/U1) of 0.6, a maximum Reynolds number (Reδ) of about 3150 and laminar initial boundary layers was generated in a mixing layer wind tunnel. Acoustic forcing, consisting of a fundamental roll-up frequency and its subharmonic, was used to phase-lock the initial development and first pairing of the spanwise vortical structures. For the first time, phase-averaged measurements of all three velocity components have been obtained on a three-dimensional grid, yielding the spanwise and streamwise vorticity distributions without invoking Taylor's hypothesis. The phase-averaged results show that the streamwise vorticity first appears in the form of ‘ribs’ just upstream of the first spanwise vortex roll-up. At the same time, the first spanwise roller becomes kinked, thus also contributing to the streamwise vorticity. As a result, in cross-stream cuts through the spanwise rollers, the streamwise vorticity appears in a ‘three-tier’ arrangement with opposite-signed vorticity in the centre. In terms of phase-averaged quantities, the maximum streamwise vorticity in the initial ribs is equivalent to about 10–15% of the peak spanwise vorticity and the streamwise rib circulation is equivalent to about 5–10% of the spanwise circulation. Further downstream, the peak streamwise vorticity decreases with increasing distance, while the average circulation remains approximately constant. Downstream of the pairing, the streamwise vorticity levels in the spanwise rollers are reduced. However, the spanwise spacing of the streamwise vortices does not increase within the measurement domain. Phase-averaged Reynolds stress measurements show that relatively high stress levels (periodic and random) were generated in the cores of the spanwise vortices.

Direct simulations of the transitional regime of a circular jet

Accurate numerical simulations of temporal evolving round jets at a low Reynolds number have revealed the same features observed in experiments and vortex filament simulations. The initial layer of azimuthal vorticity, by the Kelvin–Helmholtz instability, produces vortex rings undergoing successive pairings leading to larger rings. Axisymmetric simulations have shown that the initial roll-up is not affected by the Reynolds number, consequently insights of practical importance on the transitional regime, can be obtained from low Reynolds number simulations affordable by numerics. The 3-D simulations displayed the formation of longitudinal structures, and their role in the spreading of the jet is described. Streamwise rib vortices develop in the braid region and these vortices are responsible for the creation of small scales, premonitory of turbulence. In analogy to the plane mixing layer, the pairing reduces the growth of longitudinal and radial vorticity components and triggers the transition to turbulence. Finally comparisons between azimuthal vorticity and passive scalar surfaces have revealed that the latter collects in fat structures while the vorticity is found in thin regions where it is augmented by stretching.

Numerical Simulation of Round Jet.

A direct numerical simulation was conducted for temporally developing three-dimensional round jets, assuming periodicity in all directions of rectilinear coordinates. Two cases of nearly axi-symmetric and helical perturbations superposed on a thin round mixing layer were taken as the initial flow conditions. Subsequent evolutions of jets depending on the two initial perturbations are described, especially for coherent structures. In the case of the nearly axi-symmetric perturbation, discrete ring like rolls and streamwise ribs connecting the rolls are generated, and increases in enstrophy and helicity are primarily due to the streamwise vortex in the roll. In the case of the helical perturbation, the generation of structures is earlier than in the nearly axi-symmetric case, and rates of increase in enstrophy and helicity are lower because of the long-lived coherent structure of elongated vortices between rolls.

Erratum: ‘‘Behavior of streamwise rib vortices in a three-dimensional mixing layer’’ [Phys. Fluids A 5, 1694 (1993)

Erratum: ‘‘Behavior of streamwise rib vortices in a three-dimensional mixing layer’’ [Phys. Fluids A <b>5</b>, 1694 (1993)

On the behavior of velocity gradient tensor invariants in direct numerical simulations of turbulence

Studies of direct numerical simulations of incompressible, homogeneous, and inhomogeneous turbulence indicate that, in regions of high kinetic energy dissipation rate, the geometry of the local velocity gradient field has a universal character. The velocity gradient tensor satisfies the nonlinear evolution equation (dAij/dt)+AikAkj−1/3 (AmnAnm)δij=Hij where Aij=∂ui/∂xj and the tensor Hij contains terms involving the action of cross derivatives of the pressure field and viscous diffusion of Aij. The restricted Euler equation corresponding to Hij=0 can be solved in closed form [Cantwell, Phys. Fluids A 4, 782 (1992)] and the solution has the property that, for any initial condition, Aij(t) evolves to an asymptotic state of the form Aij(t)≂Kij[R(t)]1/3 where R(t) is a function which becomes singular in a finite time and Kij is a constant matrix. A number of the universal features of fine-scale motions observed in direct numerical simulations are reproduced by Kij. In the simulation studies the first invariant of Aij is zero by incompressibility. The second and third invariants, Q and R, are determined at every grid point in the flow and the entire data set is cross-plotted to search for significant features in the space of tensor invariants. Such features can then be associated with corresponding local flow structures in physical space. When a variety of incompressible simulations are studied, scatter plots of Q vs R reveal that a fairly significant fraction of the data lies in the lower right quadrant. This is consistent with behavior predicted by the restricted Euler solution. However, the bulk of the data lies more or less uniformly distributed in a slightly elliptical region about the origin. In a direct numerical simulation of a plane, time-developing, mixing layer a small fraction of the data collects along a very pronounced, nearly straight, ridgeline extending into the upper left quadrant. This data can be traced to regions with local vorticity much larger than the local strain lying within streamwise rib vortices which connect adjacent spanwise rollers in the mixing layer simulation. Neither the predominant tendency for Q and R to lie near the origin nor the possibility for Q and R to lie far from the origin in the upper left quadrant are predicted by the restricted Euler solution. The purpose of this paper is to show that, by relaxing the assumption Hij=0 while retaining a model of dAij/dt motivated by the asymptotic form of the restricted Euler solution, one can begin to account for these features of the (Q,R) scatter plots. The results suggest that the velocity gradient tensor in three-dimensional flow tends to evolve toward an attractor in the space of tensor invariants. A significant feature of the model is that, although Hij≠0, singular behavior of Aij(t) can still occur along specific paths in the (Q,R) plane corresponding to zero values of the discriminant of Hij.

Behavior of streamwise rib vortices in a three-dimensional mixing layer

The structure and behavior of a streamwise rib vortex in a direct numerical simulation of a time-developing three-dimensional incompressible plane mixing layer is examined. Where the rib vortex is being stretched, the vorticity vector is primarily directed in the vortex axial direction and the radial and azimuthal velocity distribution is similar to that of a Burgers vortex. In the region where the vortex stretching is negative, there is a change in the local topology of the vortex. The axial flow is decelerated and a negative azimuthal component of vorticity is induced. These features are characteristic of vortex breakdown. The temporal evolution of the rib vortex is similar to the evolution of an axisymmetric vortex in the early stages of vortex breakdown. The effect of vortex breakdown on other parts of the flow is, however, not as significant as the interaction between the rib vortex and other vortical structures.