Turbulent flow in a duct with cusped corners

An orthogonal-cuvilinear-mesh-based finite volume calculation method has been applied to the problem of fully developed turbulent flow in the tri-cusped cornered duct formed when parallel circular rods touch in triangular array. Algebraic stress relations combined with the k-? turbulence model are used for calculation of the required stresses. A single circulation of turbulence-driven cross-plane secondary flow from the core into the duct corner has been predicted in a one-sixth symmetry region of the duct and the convective transport effects of this flow are seen to have much influence on local mean flow distributions. The turbulence field predicted by the k-? model showed significant damping in the cusped corner region where turbulent viscosities approached the laminar value. Satisfactory agreement was obtained with the limited local and overall mean flow measurements available.     

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.     

The near-corner mass transfer associated with turbulent flow in a square duct

Mass transfer to a nearly fully developed turbulent flow in a square duct is studied. Measurements are taken either on one or two adjacent walls in the region of a developing mass transfer boundary layer. Effects of the secondary flow on mass transfer are observed near the corners. The effects are initially small, but grow to a significant degree further downstream. The location of the maximum and its lateral spread is affected by the Reynolds number, as well as the adjacent wall mass transfer.

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Stoffübertragung in der Nähe einer Ecke bei turbulenter Strömung in einem quadratischen Rohr

Zusammenfassung Es wird über den Massentransport in einer nahezu vollentwickelten turbulenten Strömung in einem Kanal mit quadratischem Querschnitt berichtet. Messungen werden an einer oder an zwei benachbarten Wänden im Bereich der sich entwickelnden Massenübergangsgrenzschicht durchgeführt. Im Bereich der Kanalecken werden Effekte der Sekundärströmung beobachtet. Diese Effekte sind anfänglich gering, wachsen jedoch weiter stromabwärts beträchtlich an. Die Lage des Maximums und seine laterale Ausbreitung werden sowohl durch die Reynoldszahl als auch durch den benachbarten Massenübergang zur Wand beeinflußt.

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Nomenclature D Duct's span - Dh Hydraulic diameter - Re Reynolds number (U _bulk Dh/v) - Sh Sherwood number - U Axial velocity - U _bulk Bulk velocity - x, y, z Coordinate system, Fig. 1 - x Axial distance from the duct's inlet - Kinematic viscosity Dedicated to Prof. Dr.-Ing. U. Grigull's 80th birthday     

Numerical calculation of Reynolds stresses in a square duct with secondary flow

A new model for the Reynolds stress equations is presented. This model is used to obtain a theoretical solution for the problem of fully developed turbulent flow in a square duct. Nine governing equations for the axial velocity, lateral vorticity, lateral stream function and six components of the Reynolds stresses are simultaneously solved, by a finite-difference technique. To ensure numerical stability of the solution a special linearised implicit representation of the source terms is proposed, and simultaneous solution of the equations at each.mesh point is obtained. Near the wall a special procedure is used, by which the Reynolds stress equations are assumed to be in local equilibrium, and the velocity profile is assumed to be logarithmic. However, due to the secondary motion the logarithmic velocity profile is inclined to the axial direction. The results bear reasonable agreement with experimental data. Computer time requirements are moderate.     

Analytic solution for secondary flow with heat transfer in a square duct

Analytic solutions are obtained by solving the conservation equations describing fully developed parabolic laminar flow with heat transfer to predict the axial velocity profile, the temperature distribution and the secondary flow behaviour in a square duct. The biharmonic equation arising in this problem has been solved by using the Navier method for simply supported rectangular plates. The analytic solutions substantially agree with the available experimental results.     

Turbulent forced convection in a helically coiled square duct with one uniform temperature and three adiabatic walls

In this study, effects of geometrical parameters on the average convection heat transfer characteristics in helical square ducts were investigated both experimentally and numerically. The inner wall of the helical square duct was uniformly temperatured, and the top, bottom, and outer walls were adiabatic. The Renormalization Group (RNG) k–ε turbulence model was used to simulate turbulent flow and heat transfer. The governing equations were solved by a finite volume method. Numerical results were found to be in good agreement with the presented experimental data. The new correlation was proposed for the average heat transfer coefficient on the inner wall of the helical square duct. The results showed that the ratio of pitch to coil radius b/R has no obvious effect on the inner wall convective heat transfer coefficient but the ratio of hydraulic radius to coil radius a/R has considerable effect.     

Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques

An experimental investigation on flow around an oscillating bubble and solid ellipsoid with a flat bottom was conducted. A single air bubble (equivalent diameter D_e=9.12 mm) was attached to a small disk (1 mm) at the end of a needle and suspended across a vertical square channel (100 mm) by wire wherein water flowed downward at a constant flowrate. The solid ellipsoid (D_e9.1 mm) was suspended across the square channel in the same manner. The equivalent diameter-based Reynolds and Eotvos number range, 1950<Re<2250 and 11<Eo<11.5, placed the bubble in the ‘wobbly’ regime while the flow in its wake was turbulent. A constant flowrate and one bubble size was used such that flow in the wake was turbulent. Velocity measurements of the flow field around the bubble or solid were made using a one CCD camera Digital Particle Image Velocimetry (DPIV) system enhanced by Laser Induced Fluorescence (LIF). The shape of the bubble or solid was simultaneously recorded along with the velocity using a second CCD camera and an Infrared Shadow Technique (IST). In this way both the flow-field and the boundary of the bubble (solid) were measured. The velocity vector plots of flow around and in the wake of a bubble/solid, supplemented by profiles and contours of the average and root-mean-square velocities, vorticity, Reynolds stress and turbulent kinetic energy, revealed differences in the wake flow structure behind a bubble and solid. One of the significant differences was in the inherent, oscillatory motion of the bubble which not only produced vorticity in the near-wake, but as a result of apparent vorticity stretching distributed the turbulent kinetic energy associated with this flow more uniformly on its wake, in contrast to the solid.     

Turbulent flow past a bubble and an ellipsoid using shadow-image and PIV techniques

An experimental investigation on flow around an oscillating bubble and solid ellipsoid with a flat bottom was conducted. A single air bubble (equivalent diameter D_e=9.12 mm) was attached to a small disk (∼1 mm) at the end of a needle and suspended across a vertical square channel (100 mm) by wire wherein water flowed downward at a constant flowrate. The solid ellipsoid (D_e∼9.1 mm) was suspended across the square channel in the same manner. The equivalent diameter-based Reynolds and Eotvos number range, 1950<Re<2250 and 11<Eo<11.5, placed the bubble in the ‘wobbly’ regime while the flow in its wake was turbulent. A constant flowrate and one bubble size was used such that flow in the wake was turbulent. Velocity measurements of the flow field around the bubble or solid were made using a one CCD camera Digital Particle Image Velocimetry (DPIV) system enhanced by Laser Induced Fluorescence (LIF). The shape of the bubble or solid was simultaneously recorded along with the velocity using a second CCD camera and an Infrared Shadow Technique (IST). In this way both the flow-field and the boundary of the bubble (solid) were measured. The velocity vector plots of flow around and in the wake of a bubble/solid, supplemented by profiles and contours of the average and root-mean-square velocities, vorticity, Reynolds stress and turbulent kinetic energy, revealed differences in the wake flow structure behind a bubble and solid. One of the significant differences was in the inherent, oscillatory motion of the bubble which not only produced vorticity in the near-wake, but as a result of apparent vorticity stretching distributed the turbulent kinetic energy associated with this flow more uniformly on its wake, in contrast to the solid.     

Temperature statistics in a radiatively heated particle-laden turbulent square duct flow

Radiation absorption by preferentially concentrated particles in a turbulent square duct flow is studied experimentally. The particle-laden flow is exposed to near-infrared radiation, and the gas phase temperature statistics are measured along the wall bisector of the duct. It is found that the instantaneous temperature fluctuations are comparable to the overall mean temperature rise. The temperature statistics at the duct centerline and near the wall are qualitatively different. The former reflects preferential concentration in isotropic flows while the latter displays evidence of particle clustering into streamwise elongated streaks. Comparison of the experimental data to a simplified heat transfer model suggests that the Lagrangian evolution of particle clusters and voids, and turbulent mixing in the vicinity of particle clusters, are important. This work was motivated by particle solar receiver technology, but the findings are also relevant to systems where there is localized heat release or mass transfer from disperse particles or droplets. It shows that obtaining Lagrangian histories of particle trajectories is an important next step towards understanding thermal transport phenomena in particle-laden turbulent flows.     

Measurements of turbulent developing flow in a moderately curved square duct

Laser-Doppler measurements in the turbulent flow in a right-angled bend of square cross-section, radius/duct-width ratio 7.0, are presented and show the development of secondary circulation in cross-stream planes. Distribution of the streamwise and radial components of the mean velocity and turbulence intensity, and the corresponding Reynolds shear stress, are presented as contour plots and are intended for use in the further development of numerical flow prediction methods.     

PIV measurement of separated flow over a blunt plate with different chord-to-thickness ratios

The influence of the chord-to-thickness ratio (c/t) on the spatial characteristics of the separated shear layer over a blunt plate and the leading-edge vortices embedded in the separated shear layer was studied extensively using planar particle image velocimetry (PIV). Three systems corresponding to different shedding modes were chosen for the comparative study: c/t=3, 6 and 9. The Reynolds number based on the plate's thickness (t) was Re_t=1×10³. A gigapixel CCD camera was used to acquire images with a spatial resolution of 0.06t×0.06t in the measurement range of 9.5t×4.5t. Distributions of statistical quantities, such as the streamline pattern, streamwise velocity fluctuation intensity, shear stress and reverse flow intermittency, showed that the separated shear layer in the system with c/t=3 did not reattach to the plate's surface, while the near‐wake behind the trailing edge was highly unstable because the energetic leading-edge vortices were shed into the wake. The separated shear layer of the system with c/t=6 periodically reattached to the plate's surface, which resulted in intensified fluctuations of the near wake behind the trailing edge. In the longest system (c/t=9), the separated shear layer always reattached to the plate's surface far upstream from the trailing edge, which did not induce large fluctuations of the near wake. Furthermore, the proper orthogonal decomposition (POD) was extensively employed to filter the original velocity fields spatially to identify the large-scale vortices immersed in the separated shear layer easily. The distribution of the v-v correlation coefficients of the spatially filtered flow fields reflected the organized large-scale vortices in the three systems. The number of alternations of the positive and negative correlation coefficients across the flow field were determined to be 1, 2 and 3 for the systems with c/t=3, 6 and 9, respectively; this is in agreement with the shedding mode of each system. The distribution of the swirling strength of the separated shear layer accurately determined the positions and structures of the large-scale vortices formed above the plate surface.     

Numerical simulation of magnetohydrodynamic flow in a toroidal duct of square cross-section

We present numerical simulation results of the quasi-static magnetohydrodynamic (MHD) flow in a toroidal duct of square cross-section with insulating Hartmann walls and conducting side walls. Both laminar and turbulent flows are considered. In the case of steady flows, we present a comprehensive analysis of the secondary flow. It consists of two counter-rotating vortex cells, with additional side wall vortices emerging at sufficiently high Hartmann number. Our results agree well with existing asymptotic analysis. In the turbulent regime, we make a comparison between hydrodynamic and MHD flows. We find that the curvature induces an asymmetry between the inner and outer side of the duct, with higher turbulence intensities occurring at the outer side wall. The magnetic field is seen to stabilize the flow so that only the outer side layer remains unstable. These features are illustrated both by a study of statistically averaged quantities and by a visualization of (instantaneous) coherent vortices.     

Measurement of a microchamber flow by using a hybrid multiplexing holographic velocimetry

A hybrid multiplexing holographic velocimetry used for characterizing three-dimensional, three-component (3D–3C) flow behaviors in microscale devices was designed and tested in this paper. Derived from the concept of holographic particle image velocimetry (HPIV), a new experimental facility was realized by integrating a holographic technique with a state-of-the-art multiplexing operation based on a microPIV configuration. A photopolymer plate was adopted as an intermedium to record serial stereoscopic images in the same segment. The recorded images were retrieved by a scanning approach, and, afterwards, the distributions of particles in the fluid were analyzed. Finally, a concise cross-correlation algorithm (CCC) was used to analyze particle movement and, hence, the velocity field, which was visualized by using a chromatic technique. To verify practicability, the stereoscopic flow in a backward facing step (BFS) chamber was measured by using the new experimental setup, as well a microPIV system. The comparison indicated that the photopolymer-based velocimetry was practicable to microflow investigation; however, its accuracy needed to be improved.     

Digital holographic microscopy applied to measurement of a flow in a T-shaped micromixer

In this paper, we describe measurements of a three-dimensional (3D) flow in a T-shaped micromixer by means of digital holographic microscopy. Imaging tracer particles in a microscopic flow with conventional microscopy is accompanied by a small depth-of-field, which hinders true volumetric flow measurements. In holographic microscopy, the depth of the measurement domain does not have this limitation because any desired image plane can be reconstructed after recording. Our digital holographic microscope (DHM) consists of a conventional in-line recording system with an added magnifying optical element. The measured flow velocity and the calculated vorticity illustrate four streamwise vortices in the micromixer outflow channel. Because the investigated flow is stationary and strongly 3D, the DHM performance (i.e. accuracy and resolution) can be precisely investigated. The obtained Dynamic spatial range and Dynamic velocity range are larger than 20 and 30, respectively. High-speed multiple-frame measurements illustrate the capability to simultaneously track about 80 particles in a volumetric measurement domain.     

Direct numerical simulation of turbulent flow and heat transfer in a square duct with natural convection

In this paper, a direct numerical simulation of a fully developed turbulent flow and heat transfer are studied in a square duct with an imposed temperature difference between the vertical walls and the perfectly insulated horizontal walls. The natural convection is considered on the cross section in the duct. The numerical scheme employs a time-splitting method to integrate the three dimensional incompressible Navier-Stokes equation. The unsteady flow field was simulated at a Reynolds number of 400 based on the Mean friction velocity and the hydraulic diameter (Re _m = 6200), while the Prandtl number (Pr) is assumed 0.71. Four different Grashof numbers (Gr = 10⁴, 10⁵, 10⁶ and 10⁷) are considered. The results show that the secondary flow and turbulent characteristics are not affected obviously at lower Grashof number (Gr ≤ 10⁵) cases, while for the higher Grashof number cases, natural convection has an important effect, but the mean flow and mean temperature at the cross section are also affected strongly by Reynolds stresses. Compared with the laminar heat transfer at the same Grashof number, the intensity of the combined heat transfer is somewhat decreased.     

Flow visualization and LDV measurements of laminar flow in a helical square duct with finite pitch

Flow visualization and LDV measurements are performed on laminar flow in a helical square duct with finite pitch. The experimental observations are compared to results of numerical calculations employing the finite-volume method and assuming a fully developed flow. Good agreement is found between measured and computed velocity profiles. This suggests that the physical velocity components used in the numerical calculations are suitable to describe the flow. It is further demonstrated that the contravariant velocity components employed by some authors may lead to results that are difficult to interpret. Two stable solution branches are detected in the numerical calculations. For Reynolds numbers between the stable branches, unsteady and fully developed computations predict an oscillating flow between a two-vortex and a four-vortex structure. In the experiments, the flow normally retained a stable two-vortex structure in the numerically predicted unstable regime. However, by disturbing the flow at the duct inlet, a four-vortex flow that showed similarities to the computed flow could occasionally be obtained. For Reynolds numbers above 600, unsteady flow behavior was observed both experimentally and numerically, which might be an early sign of transition. In the experiments, Gdrtler-like extra vortices emerged spontaneously from the outer wall without disturbing the flow at the inlet. The same phenomenon was observed in the numerical calculations, assuming an unsteady and fully developed flow, but the extra vortices appeared with a lower frequency than in the experiments.     

3D holographic PIV with a forward-scattering laser sheet and stereoscopic analysis

 A new 3D PIV system combining holography and stereoscopic PIV is presented. The double pulsed holographic recording relies on the forward scattering of particles in the laser sheet. The holographic images of the particles are used for a stereoscopic PIV analysis. An imaging system with a rightangle prism is used to acquire a stereoscopic pair of images. The application of the system to the vortex flow from an inclined delta wing shows the prospects and limitations of the technique. Received: 23 December 1996/Accepted: 1 June 1997     

PIV measurement of flow around an arbitrarily moving body

This paper presents a PIV (particle image velocimetry) image processing method for measuring flow velocities around an arbitrarily moving body. This image processing technique uses a contour-texture analysis based on user-defined textons to determine the arbitrarily moving interface in the particle images. After the interface tracking procedure is performed, the particle images near the interface are transformed into Cartesian coordinates that are related to the distance from the interface. This transformed image always has a straight interface, so the interrogation windows can easily be arranged at certain distances from the interface. Accurate measurements near the interface can then be achieved by applying the window deformation algorithm in concert with PIV/IG (interface gradiometry). The displacement of each window is evaluated by using the window deformation algorithm and was found to result in acceptable errors except for the border windows. Quantitative evaluations of this method were performed by applying it to computer-generated images and actual PIV measurements.     

In-Nozzle Measurements of a Turbulent Opposed Jet Using PIV

Turbulent opposed jet burners are an excellent test case for combustion research and model development due to the burners’ compactness, relative simplicity, and the good optical access they provide. The flow-field in the flame region depends strongly on the turbulence generation inside the nozzles, so that realistic flow simulations can only be achieved if the flow inside the nozzles is represented correctly, which must be verified by comparison to suitable experimental data. This paper presents detailed particle image velocimetry (PIV) measurements of the flow issuing from the turbulence generating plates (TGP) inside a glass nozzle. The resulting data is analyzed in terms of first and second moments, time-series, frequency spectra and phase averages. The measurements show how individual high velocity jets emerging from the TGP interact and recirculation zones are formed behind the solid parts of the TGP. Vortex shedding is observed in the jet’s shear layer were high levels of turbulent kinetic energy are generated. Time series measurements revealed periodic pulsations of the individual jets and implied a coupling between adjacent jets. The peak frequencies were found to be a function of the Reynolds-number.