Duct Of Square Cross-section Research Articles

Heat transfer and fluid flow through a ribbed passage in staggered arrangement

Fluid flow and heat transfer are computed through a rib-roughened duct of square cross-section. The staggered ribs are attached along the two opposite walls of the channel to augment heat transfer....

Numerical study of stability and transient phenomena of Poiseuille flows in ducts of square cross-sections

The temporal stability of Poiseuille flows in ducts of square cross-sections has been numerically studied. A new classification of disturbances based on their symmetries has been proposed. Stability characteristics such as location of leading eigenvalues, shape of eigenmodes, values of maximal energy growth, and critical Reynolds numbers have been computed.

Numerical study of Dean vortices in developing Newtonian and viscoelastic flows through a curved duct of square cross-section

This study is devoted to the three-dimensional numerical simulation of developing secondary flows of Newtonian and viscoelastic fluids through a curved duct of square cross-section. The Phan-Thien–Tanner (PTT) model is used to represent viscoelastic effects. The numerical method uses a finite volume discretization with a staggered grid, and the equations are written in general orthogonal coordinates. The numerical simulations produced for 3 different Dean numbers (125, 137 and 150) show clearly the presence of two steady Dean cells and the upstream development of a four-cell pattern when the centrifugal forces become significant. The comparison between Newtonian and PTT flows shows that the transition from twin-cells to four-cells is anticipated for the viscoelastic fluid. To cite this article: M. Boutabaa et al., C. R. Mecanique 337 (2009).

Traveling-wave solutions of the flow in a curved-square duct

Three-dimensional (3D) calculations of the flow through a curved duct of square cross section are conducted by use of the spectral method. The main concern of this paper is to clarify 3D structures of periodic solutions which have been obtained by two-dimensional (2D) calculations assuming uniformity in the main-flow direction. It is found that traveling-wave solutions are realized by 3D numerical simulations in the parameter region where periodic solutions were obtained by 2D simulations. Exact traveling-wave solutions are obtained by the iteration method from an initial guess given by the time-evolution calculations. The flow patterns of a 3D traveling wave observed in a cross section are very similar to those of 2D periodic solutions.

An optimal path to transition in a duct

This paper is concerned with the transition of the laminar flow in a duct of square cross section. As in the similar case of pipe flow, the motion is linearly stable for all Reynolds numbers, rendering this flow a suitable candidate for a study of the 'bypass' path to turbulence. It has already been shown that the classical linear optimal perturbation problem, yielding optimal disturbances in the form of longitudinal vortices, fails to provide an 'optimal' path to turbulence, i.e. optimal perturbations do not elicit a significant nonlinear response from the flow. Previous simulations have also indicated that a pair of travelling waves generates immediately, by nonlinear quadratic interactions, an unstable mean flow distortion, responsible for rapid breakdown. By the use of functions quantifying the sensitivity of the motion to deviations in the base flow, the optimal travelling wave associated with its specific defect is found by a variational approach. This optimal solution is then integrated in time and shown to display a qualitative similarity to the so-called 'minimal defect', for the same parameters. Finally, numerical simulations of an 'edge state' are conducted, to identify an unstable solution that mediates laminar-turbulent transition and relate it to results of the optimization procedure.

Experimental and CFD studies of fluid dynamic gauging in duct flows

Experimental and computational fluid dynamics (CFD) studies of the technique of fluid dynamic gauging (FDG) in duct flows have been performed. Experiments were performed using a stainless steel gauging nozzle located on the centreline of a Perspex duct of square cross section. The test fluid was water, flowing through the duct at 0.0077–0.74 m/s ( Re duct 116–11 100). The success of the experiments was confirmed by the results of Tuladhar et al. [2003. Dynamic gauging in duct flows. Canadian Journal of Chemical Engineering 81, 279-284]. For the first time, CFD has been applied to simulate FDG in an imposed flow for steady, incompressible, laminar flows. Experimental data and simulation results agreed to within 6%, supporting the validity of both the experiments and the assumptions underpinning the simulation. CFD simulations predicted the stresses beneath the lip of the nozzle and confirmed the practical working range of the gauge (0.1< h/d t <0.25). This is a major achievement, proving that CFD can be used to model this flow-FDG accurately, which is valuable for future work in this area, namely fouling in food, crude oil and cross-flow membrane systems.

Prediction of Flow and Heat Transfer through Stationary and Rotating Ribbed Ducts Using a Non-linear k−ε Model

The present paper deals with the prediction of three-dimensional fluid flow and heat transfer in rib-roughened ducts of square cross-section, which are either stationary, or rotate in orthogonal mode. The main objective is to assess how a recently developed variant of a cubic non-linear k−e model (proposed by Craft et al. Flow Turbul Combust 63:59–80, 1999) can predict three-dimensional flow and heat transfer characteristics through stationary and rotating ribbed ducts. The present paper discusses turbulent air flow and heat transfer through two different configurations, namely: (I) a stationary square duct with “in-line” normal and (II) a square duct with normal ribs in a “staggered” arrangement under stationary and rotating conditions, with the axis of rotation normal to the flow direction and parallel to the ribs. In this paper the flow and thermal predictions of the linear k−e model (EVM) are also included, as a set of baseline predictions. The mean flow predictions show that both linear and non-linear k−e models can successfully reproduce most of the measured data for stream-wise and cross-stream velocity components. Moreover, the non-linear model is able to produce better results for the turbulent stresses. The heat transfer predictions show that both EVM and NLEVM2, the more recent variant of the non-linear k−e, with the algebraic length-scale correction term, overestimate the measured Nusselt numbers for both geometries examined. While the EVM with the differential length-scale correction term underestimates heat transfer levels, the Nusselt number predictions with the NLEVM2 and the ‘NYP’ term are in close agreements with the measured data. Comparisons with our earlier work, Iacovides and Raisee (Int J Heat Fluid Flow, 20:320–328, 1999), show that the NLEVM2 thermal predictions are of similar quality to those of a second-moment closure.

Transition to turbulence in duct flow

The transition of the flow in a duct of square cross-section is studied. Like in the similar case of the pipe flow, the motion is linearly stable for all Reynolds numbers; this flow is thus a good candidate to investigate the ‘bypass’ path to turbulence. Initially the so-called ‘linear optimal perturbation problem’ is formulated and solved, yielding optimal disturbances in the form of longitudinal vortices. Such optimals, however, fail to elicit a significant response from the system in the nonlinear regime. Thus, streamwise-inhomogeneous sub-optimal disturbances are focused upon; nonlinear quadratic interactions are immediately caused by such initial perturbations and an unstable streamwise-homogeneous large-amplitude mode rapidly emerges. The subsequent evolution of the flow, at a value of the Reynolds number at the boundary between fully developed turbulence and relaminarization, shows the alternance of patterns with two pairs of large-scale vortices near opposing parallel walls. Such edge states bear a resemblance to optimal disturbances.

Experimental assessment of the effects of Prandtl number and of a guide vane on the thermal development in a ribbed square-ended U-bend

This is an experimental study of the thermal development in a stationary cooling passage which consists of two straight ducts of square cross section, with inclined ribs on two opposite sides connected by a square-ended U-bend. The upstream and downstream straight sections are 10 hydraulic diameters long. The ribs are of a square cross-section and oriented at 45° with the duct axis. The ratio between the rib height and the duct diameter, e / D H , is 0.1 and the rib spacing, P / e , is 10. First, heat transfer data obtained using air as the working fluid are compared with experimental and numerical data from our earlier work, which were obtained using water, in order to explain how the flow develops through such passages and how the Prandtl number influences the thermal characteristics. Further heat transfer measurements and flow visualisation diagrams obtained with a 180° guide vane inserted in the U-bend demonstrate the changes caused to the flow and thermal development and also enable us to assess whether the inclusion of a 180° guide vane would improve the uniformity of the local coefficient of wall heat flux. Over a Prandtl number range from 0.7 to 5.9, it is shown that the main features in the local Nusselt number variation remain the same. At higher Prandtl numbers, when scaled through the Dittus–Boelter correlation, Nusselt number levels fall and also display a steeper variation within the rib intervals. Over the end wall, Nusselt number levels are found to be considerably higher over the upstream half, probably due to flow impingement. The introduction of a 180° guide vane is shown to result in a marked increase in the Nusselt number levels within the bend, especially along the right and end walls. There is, however, a severe attenuation of the Nusselt number along both ribbed walls after the bend.

Forced convection in tightly coiled ducts: Bifurcation in a high Dean number region

The present numerical study is on the fully developed bifurcation structure of forced convection in a tightly coiled duct of square cross-section and curvature ratio of 0.5 in a high Dean number region. Ten solution branches, two symmetric and eight asymmetric, are found. Among them, one symmetric branch and seven asymmetric branches have not been reported in the literature. On these new branches, the flow has a structural 2-, 4-, 5-, 6-, 7- or 8-cell. The mean friction factor and Nusselt number are different on various solution branches. In tightly coiled ducts, the secondary flow enhances the heat transfer more significantly than the friction increase.

Effects of temperature-dependent viscosity variation on entropy generation, heat and fluid flow through a porous-saturated duct of rectangular cross-section

Effect of temperature-dependent viscosity on fully developed forced convection in a duct of rectangular cross-section occupied by a fluid-saturated porous medium is investigated analytically. The Darcy flow model is applied and the viscosity-temperature relation is assumed to be an inverse-linear one. The case of uniform heat flux on the walls, i.e. the H boundary condition in the terminology of Kays and Crawford [12], is treated. For the case of a fluid whose viscosity decreases with temperature, it is found that the effect of the variation is to increase the Nusselt number for heated walls. Having found the velocity and the temperature distribution, the second law of thermodynamics is invoked to find the local and average entropy generation rate. Expressions for the entropy generation rate, the Bejan number, the heat transfer irreversibility, and the fluid flow irreversibility are presented in terms of the Brinkman number, the Peclet number, the viscosity variation number, the dimensionless wall heat flux, and the aspect ratio (width to height ratio). These expressions let a parametric study of the problem based on which it is observed that the entropy generated due to flow in a duct of square cross-section is more than those of rectangular counterparts while increasing the aspect ratio decreases the entropy generation rate similar to what previously reported for the clear flow case by Ratts and Raut [14].

Bifurcation diagram for two-dimensional steady flow and unsteady solutions in a curved square duct

Flows through a curved duct of square cross-section are numerically studied by using the spectral method, and covering a wide range of curvature δ of the duct ( 0 < δ ⩽ 0.5 ) and the Dean number Dn ( 0 < Dn ⩽ 8000 ), where δ is non-dimensionalized by the half width of the square cross-section. The main concern is the relationship between the unsteady solutions, such as periodic, multi-periodic and chaotic solutions, and the bifurcation diagram of the steady solutions. It is found that the bifurcation diagram topologically changes if the curvature is increased and exceeds the critical value δ c ≈ 0.279645 , while it remains almost unchanged for δ < δ c or δ > δ c . A periodic solution is found to appear if the Dean number exceeds the bifurcation point, whether it is pitchfork or Hopf bifurcation, where no steady solution is stable. It is found that the bifurcation diagram and its topological change crucially affect the realizability of the steady and periodic solutions. Time evolution calculations as well as their spectral analysis show that the periodic solution turns to a chaotic solution if the Dn is further increased no matter what the curvature is. It is interesting that the chaotic solution is weak for smaller Dn, where the solution drifts among the steady solution branches, for larger Dn, on the other hand, the chaotic solution becomes strong, where the solution tends to get away from the steady solution branches.

MIXING IN A SQUARE AND A RECTANGULAR DUCT REGARDING SELECTION OF LOCATIONS FOR EXTRACTIVE SAMPLING OF GASEOUS CONTAMINANTS

Tests were conducted to characterize the uniformity of velocity and tracer gas profiles in a square and a rectangular duct with respect to defining the suitability of locations for single point sampling of gaseous contaminants. Several configurations, such as a straight duct with unidirectional flow at the entrance section and straight ducts preceded by mixing elements (a 90 degrees mitered bend and double 90 degrees bends in S- and U-type configurations) were tested. Results are compared with those from circular ducts. For a straight duct of square cross section, which is not preceded by a mixing element, the coefficients of variation (COV) of tracer gas concentration at 19 duct diameters downstream of the gas release location is 143% (center release of tracer gas). COVs of velocity and tracer gas concentration in a straight square duct 9.5 duct diameters downstream of a 90 degrees mitered bend are 6% and 24.3% (top inside release), respectively, which does not meet the ANSI N13.1 limit of 20% for the tracer gas COV. In case of the rectangular duct with a 3:1 (width to height) aspect ratio, COVs of velocity and tracer gas concentration at 9 duct diameters downstream of a 90 degrees mitered bend are 29% and 62% (bottom inside release), respectively. A mixing element in a square duct comprised of two 90 degrees mitered bends in a U-configuration produces results similar to those obtained with a single 90 degrees bend. However, COVs of velocity and tracer gas concentration in a square duct 6 duct diameters downstream of an S-type double bend are 10.6% and 8.3% (top inside release), respectively, which comply with the ANSI tracer gas and velocity criteria for single point representative sampling. When mixing elements were employed in square ducts, the COV results were comparable with those of other researchers for circular ducts.

Turbulent transport of particles in a straight square duct

Turbulent flow through a duct of square cross-section gives rise to off-axis secondary flows, which are known to transfer momentum between fluid layers thereby flattening the velocity profile. The aim of this study is to investigate the role of the secondary flows in the transport and dispersion of particles suspended in a turbulent square duct flow. We have numerically simulated a flow through a square duct having a Reynolds number of Re τ = 300 through discretization of the Navier–Stokes equations, and followed the trajectories of a large number of passive tracers and finite-inertia particles under a one-way coupling assumption. Snapshots of particle locations and statistics of single-particle and particle pair dispersion were analyzed. It was found that lateral mixing is enhanced for passive tracers and low-inertia particles due to the lateral advective transport that is absent in straight pipe and channels flows. Higher inertia particles accumulate close to the wall, and thus tend to mix more efficiently in the streamwise direction since a large number of the particles spend more time in a region where the mean fluid velocity is small compared to the bulk. Passive tracers tend to remain within the secondary swirling flows, circulating between the core and boundary of the duct.

Effects of Curvature and Convective Heat Transfer in Curved Square Duct Flows

Non-isothermal flows with convective heat transfer through a curved duct of square cross section are numerically studied by using a spectral method, and covering a wide range of curvature, δ, 0&lt;δ≤0.5 and the Dean number, Dn, 0≤Dn≤6000. A temperature difference is applied across the vertical sidewalls for the Grashof number Gr=100, where the outer wall is heated and the inner one cooled. Steady solutions are obtained by the Newton-Raphson iteration method and their linear stability is investigated. It is found that the stability characteristics drastically change due to an increase of curvature from δ = 0.23 to 0.24. When there is no stable steady solution, time evolution calculations as well as their spectral analyses show that the steady flow turns into chaos through periodic or multi-periodic flows if Dn is increased no matter what δ is. The transition to a periodic or chaotic state is retarded with an increase of δ. Nusselt numbers are calculated as an index of horizontal heat transfer and it is found that the convection due to the secondary flow, enhanced by the centrifugal force, increases heat transfer significantly from the heated wall to the fluid. If the flow becomes periodic and then chaotic, as Dn increases, the rate of heat transfer increases remarkably.

Developing compressible viscous flow structures in a curved duct of square cross-section

Developing compressible viscous flow structures in a curved duct of square cross-section

Visualization of Taylor–Dean flow in a curved duct of square cross-section

The secondary flow in a curved duct of square cross-section is investigated experimentally using a visualization method. Three walls of the duct (except the outer wall) rotate around the center of curvature and an azimuthal pressure gradient is imposed. Photographs of the flow in a cross-section at 180° downstream from the curved duct entrance are taken by changing the flux (Dean number) at a constant rotational speed (Taylor number) of the duct walls. Several types of secondary flow are detected. The variation of the flow patterns with change of flow parameters is compared with that of numerical calculations and is found to be in good agreement. The diagram showing types of secondary flow patterns in the Taylor–Dean number plane is obtained.

Bifurcation and stability of forced convection in tightly coiled ducts: multiplicity

A numerical study is made on the fully developed bifurcation structure of the forced convection in tightly coiled ducts of square cross-section. In addition to the examination of structural changes of three known solution branches found in loosely coiled ducts, three new solution branches are found. These new branches are isolated from the three known branches. The flows on these new branches are in a symmetric 4-cell state, a symmetric 8-cell state, an asymmetric 2-cell state, an asymmetric 5-cell state, an asymmetric 7-cell state, or an asymmetric 8-cell structure.

Validation of the LES approach in Kiva‐3V on a square duct geometry

AbstractThe LES approach implemented in the Kiva‐3V code is evaluated on the fully developed flow through a rectangular duct of square cross section. The Reynolds number based on the bulk velocity and duct width is 8000. The number of grid nodes is 96000. Three subgrid‐scale models are compared: the Smagorinsky, the WALE and the Vreman model. The results differ mainly in the predicted shear stress levels. The Smagorinsky model shows a large overprediction of the shear at the walls, whereas both the WALE and Vreman models perform better due to a reduced contribution of the subgrid dissipation. In this study the WALE model gives the best results on simulating the secondary flows and turbulence statistics. Copyright © 2005 John Wiley &amp; Sons, Ltd.

Numerical Procedure for the Laminar Developed Flow in a Helical Square Duct

The incompressible fully developed laminar flow in a helically duct of square cross section is studied expressing the governing equations in terms of an orthogonal coordinate system. Numerical results are obtained with the described continuity, vorticity, and pressure (CVP) numerical method using a colocation grid for all variables. Since there are not approximations, the interaction effects of curvature, torsion and axial pressure gradient on the velocity components and the friction factor are presented. The results show that the torsion deforms substantially the symmetry of the two centrifugal vortices of the secondary flow, which for large values of torsion combined with small curvature tend to one vortex covering the whole cross section. The friction factor decreases for torsion in the range 0 to 0.1 and increases as the torsion increases further, a behavior which is more profound as the Dean number increases. Our results are stable for the calculated Dean numbers.