Flow In Rectangular Duct Research Articles

Numerical Calculations of Liquid-Metal Magnetohydrodynamic Flows in Rectangular Ducts with Sudden Contractions

For the design of the liquid-metal blanket in a fusion reactor, numerical calculations have been carried out on liquid-metal magnetohydrodynamic flows in rectangular ducts with sudden contractions. Conservation equations of fluid mass and fluid momentum and the Poisson equation for electrical potential have been solved numerically. The numerical calculations have been conducted for a Hartmann number of ~10 000; a Reynolds number of ~10 000; and contraction ratios (CRs) of 2, 3, and 4. The pressure loss through the contraction has been estimated by the loss coefficient ζ divided by the interaction parameter N, i.e. ζ/N. The loss coefficient ζ/N through the contraction parallel to the magnetic field is much larger than that through the corresponding contraction perpendicular to the magnetic field. The loss coefficient ζ/N increases consistently with the CR and does not change very much with N. While ζ/N also does not change very much with the wall conductance ratio for the contraction parallel to the magnetic field, ζ/N increases gradually with the wall conductance ratio for the contraction perpendicular to the magnetic field.

Linear and nonlinear Granger causality analysis of turbulent duct flows

This research focuses on the identification and causality analysis of coherent structures that arise in turbulent flows in square and rectangular ducts. Coherent structures are first identified from direct numerical simulation data via proper orthogonal decomposition (POD), both by using all velocity components, and after separating the streamwise and secondary components of the flow. The causal relations between the mode coefficients are analysed using pairwise-conditional Granger causality analysis. We also formulate a nonlinear Granger causality analysis that can account for nonlinear interactions between modes. Focusing on streamwise-constant structures within a duct of short streamwise extent, we show that the causal relationships are highly sensitive to whether the mode coefficients or their squared values are considered, whether nonlinear effects are explicitly accounted for, and whether streamwise and secondary flow structures are separated prior to causality analyses. We leverage these sensitivities to determine that linear mechanisms underpin causal relationships between modes that share the same symmetry or anti-symmetry properties about the corner bisector, while nonlinear effects govern the causal interactions between symmetric and antisymmetric modes. In all cases, we find that the secondary flow fluctuations (manifesting as streamwise vorticial structures) are the primary cause of both the presence and movement of near-wall streaks towards and away from the duct corners.

Multivariate Peristalsis in a Straight Rectangular Duct for Carreau Fluids

Peristaltic flow in a straight rectangular duct is examined imposed by contraction pulses implemented by pairs of horizontal cylindrical segments with their axes perpendicular to the flow direction. The wave propagation speed is considered in such a range that triggers a laminar fluid motion. The setting is analyzed over a set of variables which includes the propagation speed, the relative occlusion, the modality of the squeezing pulse profile and the Carreau power index. The numerical solution of the equations of motion on Cartesian meshes is grounded in the immersed boundary method. An increase in the peristaltic pulse modality leads to the reduction in the shear rate levels on the central tube axis and to the movement of the peristaltic characteristics to higher pressure values. The effect of the no slip side walls (NSSWs) is elucidated by the collation with relevant results for the flow field produced under the same assumptions though with slip side walls (SSWs). Shear thinning behavior exhibits a significantly larger effect on transport efficiency for the NSSWs duct than on the SSWs duct.

Numerical Calculations of Liquid-Metal Magnetohydrodynamic Flows in Rectangular Ducts with Sudden Expansions

Relating to the design of liquid-metal blankets in a fusion reactor, numerical calculations have been performed on liquid-metal magnetohydrodynamic (MHD) flows in rectangular ducts with sudden expansions. Conservation equations of fluid mass and fluid momentum, together with the Poisson equation for electrical potential, have been solved numerically. The numerical calculations have been performed for Hartmann (Ha) numbers up to the order of 10000 and expansion ratios up to 4. The pressure loss through the expansion has been estimated by the loss coefficient ζ divided by the interaction parameter N, i.e., ζ/N. The loss coefficient ζ/N through the expansion parallel to the magnetic field is much larger than that through the expansion perpendicular to the magnetic field. The loss coefficient ζ/N increases consistently with the expansion ratio. The loss coefficient ζ/N does not change very much with the interaction parameter N and the wall conductance ratio.

Direct numerical simulation of flow in open rectangular ducts

We study turbulent flow in open channels with a free surface and rectangular cross-section, for various Reynolds numbers and duct aspect ratios. Direct numerical simulations are used to obtain accurate characterization of the secondary motions, which are found to be more intense than in closed ducts, and to scale with the bulk, rather than with the friction velocity. A notable feature of open-duct flows is the presence of a velocity dip, namely the peak velocity is achieved at some depth underneath the free surface. We find that the depth of the velocity peak increases with the Reynolds number, and correspondingly the flow becomes more symmetric with respect to the horizontal midplane. This is also confirmed from the change of the topology of the secondary motions, which exhibit a strong corner circulation at the free-surface/wall corners at low Reynolds number, which, however, weakens at higher $Re$ . The structure of the mean velocity field is such that the log law applies with good approximation in the direction normal to the nearest wall, which allows us to explain why predictive friction formulae based on the hydraulic diameter concept are successful. Additional analysis shows that the secondary motions account for a large fraction of the frictional drag (up to $15$ %).

Effects of the direction of rotation axis on turbulent flows in rectangular ducts

The effects of the direction of rotation axis on flows in rectangular ducts are studied using direct numerical simulation. The rotation axis lies in the cross section of the duct. The angle of the rotation axis relative to the bottom edge of the cross section is altered from 0° to 90°. A series of cases are considered, including three Reynolds numbers Reτ = 300, 454, and 900, three rotation numbers Roτ = 2, 4, and 8, and two cross-sectional aspect ratios ar = 1.0 and 2.0. The results show that as the angle increases, the bulk velocity remains almost constant in the square duct while it decreases monotonically in the duct with ar = 2.0. When the angle increases from 0° to 45°, turbulence is significantly or even completely suppressed, while the secondary flow is gradually enhanced. Furthermore, with the same rotation number, turbulence is more strongly suppressed at a lower Reynolds number. As the angle further increases from 45° to 90° in the cases with ar = 2.0, the intensity of turbulence is recovered to some extent and the secondary flow gradually weakens. With the angle increasing from 0°, the Ekman layer is formed above the pressure wall and gradually strengthens, resulting in a drastic wall-normal variation of the mean flow direction and a tilting of the low-speed streaks near the wall, which may cause the weakening of the turbulence. In addition, in the flow fields where turbulence is severely suppressed, periodic structures are observed in the corner of the duct, which needs further study.

Stratified inclined duct: direct numerical simulations

The stratified inclined duct (SID) experiment consists of a zero-net-volume exchange flow in a long tilted rectangular duct, which allows the study of realistic stratified shear flows with sustained internal forcing. We present the first three-dimensional direct numerical simulations (DNS) of SID to explore the transitions between increasingly turbulent flow regimes first described by Meyer & Linden (J. Fluid Mech., vol. 753, 2014, pp. 242–253). We develop a numerical set-up that faithfully reproduces the experiments and sustains the flow for arbitrarily long times at minimal computational cost. We recover the four qualitative flow regimes found experimentally in the same regions of parameter space: laminar flow, waves, intermittent turbulence and fully developed turbulence. We find good qualitative and quantitative agreement between DNS and experiments and highlight the added value of DNS to complement experimental diagnostics and increase our understanding of the transition to turbulence, both temporally (laminar/turbulent cycles) and parametrically (as the tilt angle of the duct and the Reynolds number are increased). These results demonstrate that numerical studies of SID – and deeper integration between simulations and experiments – have the potential to lead to a better understanding of stratified turbulence.

Field synergy and thermodynamic evaluation of a mini-duct with several protrusions utilizing the cross-flow method: A numerical exercise

The field synergy and entropy generation analysis of turbulent flow in a mini rectangular duct featuring surface protrusions has been numerically explored in a finite volume approach. The governing differential is solved iteratively using adequate numerical boundary conditions and a second-order upwind technique. In the post-processing, entropy generation, and irreversibilities are measured. The duct Reynolds number (ReDh, duct) has been varied from 17,831 to 53,492 at a fixed nozzle Reynolds number (ReDh, nz) of 5104. The effects of the duct Reynolds number on the thermal and frictional irreversibility have been quantified. Thermal, frictional, and total irreversibilities have been reported to rise with ReDh, duct. Furthermore, it is discovered that thermal irreversibility dominates over frictional irreversibility. It has been found that conducting triangular protrusions creates more entropy than conducting rectangular protrusions. Filed synergy analysis has also been carried out by integrating the energy equation. Heat transfer rate has been seen to increase with synergy angle (α). Triangular protrusions have a greater field synergy angle (α) than rectangular protrusions.

Molecular Interaction and Magnetic Dipole Effects on Fully Developed Nanofluid Flowing via a Vertical Duct Applying Finite Volume Methodology

Interpreting the complex interaction of nanostructured fluid flow with a dipole in a duct, with peripherally uniform temperature distribution, is the main focus of the current work. This paper also sheds light on the changes in the Nusselt number, temperature profiles, and velocity distributions for the fully developed nanofluid flow in a vertical rectangular duct due to a dipole placed near a corner of the duct. A finite volume approach has been incorporated for the numerical study of the problem. It is interesting to note the unusually lower values of the Nusselt number for the higher values of the ratio Gr/Re. Due to the nanostructure in the fluid, an enhancement in the Nusselt number has been noted, which is strongly supported by the magnetic field caused by the dipole. However, as the duct shape is transformed from rectangular to square, the Nusselt number is reduced remarkably. Further, as the dipole is brought nearer to the duct corner, the Nusselt number increases significantly. On the other hand, the flow reversal in the middle of the duct has been noted at higher values of the ratio Gr/Re. The dipole is noted to have a low impact on the reversal flow as well as on the temperature distribution.

Development and Validation of a Novel Control-Volume Model for the Injection Flow in a Variable Cycle Engine

The variable area bypass injector (VABI) plays a crucial role in variable cycle engines by regulating the flow mixing process in complex bypass ducts, and low-dimensional theoretical models are the key to revealing its working mechanism while estimating its aerodynamic performance. An improved VABI model using the control volume method is established, through which the feature parameters that determine the VABI aerodynamic performance are summarized. To acquire an accurate prediction of the injection ratio, a calibration item is introduced to the governing equations to consider the static pressure discrepancy on the mixing plane, and a numerical database is developed to obtain the calibration item. Results show that the aerodynamic parameters that determine the VABI performance include the bypass total pressure ratio, bypass backpressure, and the injection ratio, while the injection angle and the VABI opening area also influence the injection flow characteristics. The injection ratio is increased by reducing the bypass total pressure ratio, decreasing the bypass backpressure, and closing the VABI. Numerical validation shows that the calculation error of the improved model is generally below 3%. The improved VABI model is then validated by a well-arranged experiment, for which the annular flow is simplified into a rectangular duct flow with an error of less than 5%. The experimental validation also proves the accuracy of the model.

Studying the impacts of droplets depositing from the gas core onto a gas-sheared liquid film with stereoscopic BBLIF technique.

In annular gas-liquid flow, the droplets are torn from the liquid film surface by the turbulent gas stream, accelerate due to the gas drag force and eventually deposit back onto the wavy film surface, hitting it with a high speed at a shallow angle. Here we investigate individual impacts of droplets in annular flow in a horizontal rectangular duct, in a wide range of gas and liquid flow rates for three different working liquids. A stereoscopic modification of the Brightness-Based Laser-Induced Fluorescence technique is developed to reconstruct the spatiotemporal evolution of waves on the film surface in three-dimensional space, simultaneously with capturing instantaneous position, size, and three velocity components of the individual droplets and bubbles. Droplet impacts create furrows (with bubbles entrapment) and craters (with secondary droplets) on film surface. Propagation of the furrowing droplet may be facilitated by gliding on an air layer but hampered by the ripples on the film surface. The number of entrapped bubbles is mainly defined by the droplet diameter and by liquid properties. The saturation of the number of bubbles entrapped due to furrow impacts is confirmed experimentally. The secondary droplets are rarely created due to break-up of the crater crown. In most cases, the main role in secondary entrainment is played by longitudinal movement of the impacting droplet, which helps the droplet to escape the impact-created crater and detach from the film, creating various transient liquid structures, with different ways to create secondary droplets.

Numerical simulation and multi-objective optimization of heat transfer of Al2O3/water nanofluid in rectangular ducts

Laminar flow of Al2O3/water nanofluids in rectangular ducts with different aspect ratios (AR) were simulated numerically. Both heat transfer coefficient and pressure drop of nanofluids are higher than the base fluid and increase with nanofluid concentration in ducts of all aspect ratios. For a duct with AR = 2, the heat transfer coefficient of nanofluids with a concentration of 5% vol. is on average 22% higher than the base fluid. Its pressure drop is about 2.5 times of the base fluids. The effect of nanofluid concentration on the heat transfer coefficient is more significant in ducts with a lower aspect ratio. The heat transfer coefficient of a 5% vol. nanofluid in a duct with AR = 1 is about 24% larger than the base fluid; this value is about 18% for a duct with AR = 6. The effect of nanofluid concentration on the pressure drop of all ducts is identical. The results of the numerical simulation were used for training a multi-Layer perceptron artificial neural network (MLP-ANN) model. The ANN model predicts the pressure drop and heat transfer coefficient of nanofluids in rectangular ducts very accurately. The maximum differences between the values of heat transfer coefficient predicted by the ANN and those obtained from the numerical simulation is about 0.11%, and that of the pressure drop is about 0.65%. Multi-objective NSGA-II optimization algorithm was applied to optimize the nanofluid flow in rectangular ducts. In optimization, the goal was to maximize the heat transfer coefficient and minimize the pressure drop. The values of objective functions were evaluated by the resulting ANN model. Optimization for ducts with each aspect ratio was performed. Optimization was also done for all channels. Pareto fronts were obtained from optimization. The best solution for each optimization is determined by two decision-making methods. For the overall optimal solution, nanofluid concentration, Reynolds number, and the duct aspect ratio are 2.28% vol., 400, and 6, respectively which are the same as the optimal solution of the duct with an aspect ratio of six.

Pattern Transition on Inertial Focusing of Neutrally Buoyant Particles Suspended in Rectangular Duct Flows.

The continuous separation and filtration of particles immersed in fluid flows are important interests in various applications. Although the inertial focusing of particles suspended in a duct flow is promising in microfluidics, predicting the focusing positions depending on the parameters, such as the shape of the duct cross-section and the Reynolds number (Re) has not been achieved owing to the diversity of the inertial-focusing phenomena. In this study, we aimed to elucidate the variation of the inertial focusing depending on Re in rectangular duct flows. We performed a numerical simulation of the lift force exerted on a spherical particle flowing in a rectangular duct and determined the lift-force map within the duct cross-section over a wide range of Re. We estimated the particle trajectories based on the lift map and Stokes drag, and identified the particle-focusing points appeared in the cross-section. For an aspect ratio of the duct cross-section of 2, we found that the blockage ratio changes transition structure of particle focusing. For blockage ratios smaller than 0.3, particles focus near the centres of the long sides of the cross-section at low Re and near the centres of both the long and short sides at relatively higher Re. This transition is expressed as a subcritical pitchfork bifurcation. For blockage ratio larger than 0.3, another focusing pattern appears between these two focusing regimes, where particles are focused on the centres of the long sides and at intermediate positions near the corners. Thus, there are three regimes; the transition between adjacent regimes at lower Re is found to be expressed as a saddle-node bifurcation and the other transition as a supercritical pitchfork bifurcation.

Reduced models of unidirectional flows in compliant rectangular ducts at finite Reynolds number

Soft hydraulics, which addresses the interaction between an internal flow and a compliant conduit, is a central problem in microfluidics. We analyze Newtonian fluid flow in a rectangular duct with a soft top wall at steady state. The resulting fluid–structure interaction is formulated for both vanishing and finite flow inertia. At the leading-order in the small aspect ratio, the lubrication approximation implies that the pressure only varies in the streamwise direction. Meanwhile, the compliant wall's slenderness makes the fluid–solid interface behave like a Winkler foundation, with the displacement fully determined by the local pressure. Coupling flow and deformation and averaging across the cross section leads to a one-dimensional reduced model. In the case of vanishing flow inertia, an effective deformed channel height is defined rigorously to eliminate the spanwise dependence of the deformation. It is shown that a previously used averaged height concept is an acceptable approximation. From the one-dimensional model, a friction factor and the corresponding Poiseuille number are derived. Unlike the rigid duct case, the Poiseuille number for a compliant duct is not constant but varies in the streamwise direction. Compliance can increase the Poiseuille number by a factor of up to four. The model for finite flow inertia is obtained by assuming a parabolic vertical variation of the streamwise velocity. To satisfy the displacement constraints along the edges of the channel, weak tension is introduced in the streamwise direction to regularize the Winkler-foundation-like model. Matched asymptotic solutions of the regularized model are derived.

Verification and Validation of COMSOL Magnetohydrodynamic Models for Liquid Metal Breeding Blankets Technologies

Liquid metal breeding blankets are extensively studied in nuclear fusion. In the main proposed systems, the Water Cooled Lithium Lead (WCLL) and the Dual Coolant Lithium Lead (DCLL), the liquid metal flows under an intense transverse magnetic field, for which a magnetohydrodynamic (MHD) effect is produced. The result is the alteration of all the flow features and the increase in the pressure drops. Although the latter issue can be evaluated with system models, 3D MHD codes are of extreme importance both in the design phase and for safety analyses. To test the reliability of COMSOL Multiphysics for the development of MHD models, a method for verification and validation of magnetohydrodynamic codes is followed. The benchmark problems solved regard steady state, fully developed flows in rectangular ducts, non-isothermal flows, flow in a spatially varying transverse magnetic field and two different unsteady turbulent problems, quasi-two-dimensional MHD turbulent flow and 3D turbulent MHD flow entering a magnetic obstacle. The computed results show good agreement with the reference solutions for all the addressed problems, suggesting that COMSOL can be used as software to study liquid metal MHD problems under the flow regimes typical of fusion power reactors.

Experimental Study of Mixed Convection Heat Transfer to Thermally Developing Air Flow in a Horizontal Rectangular Duct

Experimental Study of Mixed Convection Heat Transfer to Thermally Developing Air Flow in a Horizontal Rectangular Duct

Experimental and Numerical Investigation of Flow and Heat Transfer in Stationary Two-Pass Rectangular Duct (AR = 1:2) With Continuous and Broken V-Shaped Ribs

Abstract The combined experimental and large eddy simulations (LES) were performed in the stationary two-pass duct of aspect ratio (AR) 1:2. The experiments were conducted with three different rib arrangements, namely, 60 deg V, 60 deg V–IV, and broken 60 deg V–IV ribs, and the analysis was carried out with Reynolds numbers of 45,000, 60,000, and 75,000. The infrared thermography (IRT) technique is employed to obtain the local temperature distribution on heated smooth and ribbed surfaces. In all ribbed cases, the copper ribs are glued to the heated surface with a fixed rib height-to-hydraulic diameter (e/Dh) ratio of 0.125 and the rib pitch-to-height ratio (P/e) of 10 and 5 for continuous and broken ribs, respectively. In addition, the LES turbulence model was adopted for carrying out a simulation to understand the flow and heat transfer behavior in ducts populated with all three V-shaped ribs. The comparison of the time-averaged thermal fields generated using computations has been made with experimentally measured Nusselt numbers, friction factors, thermal performance factor (TPF), and Reynolds analogy performance parameter (RAPP) for all cases. The overall thermal performance factor was found to be quantitatively within 8.0–10.66% between experimental and numerical results. Among all the cases, the 60 deg V–IV ribbed duct provides the best TPF and RAPP than the other two ribbed ducts, whereas the smooth duct shows poor TPF.

Characterization of heat transfer and friction loss of water turbulent flow in a narrow rectangular duct under 25–40 kHz ultrasonic waves

This study experimentally investigated the effect of low-frequency ultrasonic waves on the heat transfer augmentation of turbulent water flow in a narrow rectangular duct with a width of 5 mm. 25-, 33-, and 40-kHz ultrasonic transducers were set to release waves in a downward direction to disturb the flow, with Reynolds numbers (Re) of 10,000–25,000 at increments of 2500. The results indicated that the ultrasonic waves increased the friction loss by only 0.2–2% over the entire testing Re range, while an 8.1–48.6% enhancement of the heat transfer capability was obtained for the Re range of 10,000–15,000. The maximum Nusselt number occurred at a Re of 12,500 and frequency of 33 kHz. However, beyond Re values of 12,500, the thermal performance tended to decrease with an increase in Re. Consequently, the average Nusselt number ratios at ultrasonic frequencies of 25, 33, and 40 kHz over the tested Re range were 1.123, 1.039, and 1.033, respectively, while the thermal performance values were 1.108, 0.989, and 1.036, respectively. These results confirmed that ultrasound has significant potential for application in heat transfer augmentation of turbulent pipe flow. This paper also provides formulas to predict the friction factor and Nusselt number and discusses the mechanisms of heat transfer enhancement by ultrasonic waves at 25, 33, and 40 kHz.

Convective fluid flow and heat transfer in a vertical rectangular duct containing a horizontal porous medium and fluid layer

PurposeThe purpose of this paper is to investigate thermally and hydrodynamically fully developed convection in a duct of rectangular cross-section containing a porous medium and fluid layer.Design/methodology/approachThe Darcy–Brinkman–Forchheimer flow model is adopted. A finite difference method of second-order accuracy with the Southwell-over-relaxation method is deployed to solve the non-dimensional momentum and energy conservation equations under physically robust boundary conditions.FindingsIt is found that the presence of porous structure and different immiscible fluids exert a significant impact on controlling the flow. Graphical results for the influence of the governing parameters i.e. Grashof number, Darcy number, porous media inertia parameter, Brinkman number and ratios of viscosities, thermal expansion and thermal conductivity parameters on the velocity and temperature fields are presented. The volumetric flow rate, skin friction and rate of heat transfer at the left and right walls of the duct are also provided in tabular form. The numerical solutions obtained are validated with the published study and excellent agreement is attained.Originality/valueTo the author’s best knowledge this study original in developing the numerical code using FORTRAN to assess the fluid properties for immiscible fluids. The study is relevant to geothermal energy systems, thermal insulation systems, resin flow modeling for liquid composite molding processes and hybrid solar collectors.

Studying the Effect of Magnetic Strength and Electrical Conductivity on the Velocity Profile of an MHD Flow in a Rectangular Duct

This document presents the results of an investigation of the impact of variations of electrical conductivity and magnetic field strength on the velocity profile inside a rectangular duct, assuming equilibrium flow. It also presents the physics and the complete theory associated with the MHD, then derive the equations to be utilized for computational analysis of the magnetic field and the velocity profiles.The computational work in this document is based on the assumption that the working fluid is air and it is fully developed in the duct. The finite difference method is used to perform the analysis for 2 distinct cases: the first case is when the magnetic field strength changes, while holding the electrical conductivity constant. The second case is when the electrical conductivity is changing while holding the magnetic field strength constant.It has been found that increasing the magnetic field strength has resulted in decreasing the axial velocity profile, which demonstrated that the magnetic field was pulling the flow to its direction, reducing the flow momentum in the axial direction. It has also been found that the electrical conductivity reduced the velocity profile in the axial direction when that conductivity was increasing, demonstrating that the electric field was also pulling the flow in its direction, reducing the flow momentum in the axial direction. Keywords: MHD, Magnetohydrodynamics, Flow in Rectangular Duct, Magnetic Field, Electrical Conductivity, MHD Flow, MHD Flow Velocity Profile DOI: 10.7176/JETP/10-4-03 Publication date: August 31 st 2020