Effects of rotation on flow in an asymmetric rib-roughened duct: LES study

We report on large-eddy simulations (LES) of fully-developed asymmetric flow in a duct of a rectangular cross-section in which square-sectioned, equally-spaced ribs oriented perpendicular to the flow direction, were mounted on one of the walls. The configuration mimics a passage of internal cooling of a gas-turbine blade. The duct flow at a Reynolds number Re = 15,000 (based on hydraulic diameter D_h and bulk flow velocity U₀) was subjected to clock-wise (stabilising) and anti-clock-wise (destabilising) orthogonal rotation at a moderate rotational number Ro = ΩD_h/U₀ = 0.3, where Ω is the angular velocity. The LES results reproduced well the available experimental results of Coletti et al. (2011) (in the mid-plane adjacent to the ribbed wall) and provided insight into the whole duct complementing the reference PIV measurement. We analyzed the effects of stabilising and destabilising rotation on the flow, vortical structures and turbulence statistics by comparison with the non-rotating case. The analysis includes the identification of depth of penetration of the rib-effects into the bulk flow, influence of flow three-dimensionality and the role of secondary motions, all shown to be strongly affected by the rotation and its direction.     

Vortex mechanism of heat transfer enhancement in a channel with spherical and oval dimples

Vortex mechanism of heat transfer enhancement in a narrow channel with dimples has been investigated numerically using LES and URANS methods. The flow separation results in a formation of vortex structures which significantly enhance heat transfer on dimpled surfaces leading to a small increase in pressure loss. The heat transfer can be significantly increased by rounding the dimple edge and use of oval dimples. To get a deep insight into flow physics LES is performed for single phase flow in a channel with a spherical dimple. The instantaneous vortex formation and separation are investigated in and around the dimple area. Considered are Reynolds numbers (based on dimple print diameter) Re_D = 20,000 and Re_D = 40,000 the depth to print diameter ratio of Δ = 0.26. Frequency analysis of LES data revealed the presence of dominating frequencies in unsteady flow oscillations. Direct analysis of the flow field revealed the presence of coherent vortex structure inclined to the mean flow. The structure changes its orientation in time causing the long period oscillations with opposite-of-phase motion. Three dimensional proper orthogonal decomposition (POD) analysis is carried out on LES pressure and velocity fields to identify spatio-temporal structures hidden in the random fluctuations. Tornado-like spatial POD structures have been determined inside dimples.     

Flow instability in baffled channel flow

Flow instability in baffled channel flow, where thin baffles are mounted on both channel walls periodically in the direction of the main flow, has been numerically investigated. The geometry considered here can be regarded as a simple model for finned heat exchangers. The aim of this investigation is to understand how baffle interval (L) and Reynolds number (Re) influence the flow instability. With a fixed baffle length of one quarter of channel height (H), ratios of baffle interval to channel height (R_B = L/H) between 1 and 4 are considered. The critical Reynolds number of the primary instability, a Hopf bifurcation from steady flow to time-periodic flow, turned out to be minimum when R_B = 3.08. The friction factor (f) is strongly correlated with the critical Reynolds number for R_B ⩽ 2.5. For the particular cases of R_B = 1.456 and R_B = 1.0, we performed Floquet stability analysis in order to study the secondary instability through which time-periodic two-dimensional flow bifurcates into three-dimensional flow. The results obtained in this investigation are in good agreement with those computed from full simulations, and shed light on understanding and controlling flow characteristics in a finned heat exchanger, quite beneficial to its design.     

“Magnetic-ribs” in fully developed laminar liquid–metal channel flow

This paper documents the numerical investigation of the effects of non-uniform magnetic fields, i.e. magnetic-ribs, on a liquid–metal flowing through a two-dimensional channel. The magnetic ribs are physically represented by electric currents flowing underneath the channel walls. The Lorentz forces generated by the magnetic ribs alter the flow field and, as consequence, the convective heat transfer and wall shear stress. The dimensionless numbers characterizing a liquid–metal flow through a magnetic field are the Reynolds (Re) and the Stuart (N) numbers. The latter provides the ratio of the Lorentz forces and the inertial forces. A liquid–metal flow in a laminar regime has been simulated in the absence of a magnetic field (Re_H = 1000, N = 0), and in two different magnetic ribs configurations for increasing values of the Stuart number (Re_H = 1000, N equal to 0.5, 2 and 5). The analysis of the resulting velocity, temperature and force fields has revealed the heat transport phenomena governing these magneto-hydro-dynamic flows. Moreover, it has been noticed that, by increasing the strength of the magnetic field, the convective heat transfer increases with local Nusselt numbers that are as much 27.0% larger if compared to those evaluated in the absence of the magnetic field. Such a convective heat transfer enhancement has been obtained at expenses of the pressure drop, which increases more than twice with respect to the non-magnetic case.     

Flow evolution of a turbulent submerged two-dimensional rectangular free jet of air. Average Particle Image Velocimetry (PIV) visualizations and measurements

The paper presents average flow visualizations and measurements, obtained with the Particle Image Velocimetry (PIV) technique, of a submerged rectangular free jet of air in the range of Reynolds numbers from Re = 35,300 to Re = 2200, where the Reynolds number is defined according to the hydraulic diameter of a rectangular slot of height H. According to the literature, just after the exit of the jet there is a zone of flow, called zone of flow establishment, containing the region of mixing fluid, at the border with the stagnant fluid, and the potential core, where velocity on the centerline maintains a value almost equal to the exit one. After this zone is present the zone of established flow or fully developed region. The goal of the paper is to show, with average PIV visualizations and measurements, that, before the zone of flow establishment is present a region of flow, never mentioned by the literature and called undisturbed region of flow, with a length, L_U, which decreases with the increase of the Reynolds number. The main characteristics of the undisturbed region is the fact that the velocity profile maintains almost equal to the exit one, and can also be identified by a constant height of the average PIV visualizations, with length, L_CH, or by a constant turbulence on the centerline, with length L_CT. The average PIV velocity and turbulence measurements are compared to those performed with the Hot Film Anemometry (HFA) technique. The average PIV visualizations show that the region of constant height has a length L_CH which increases from L_CH = H at Re = 35,300 to L_CH = 4–5H at Re = 2200. The PIV measurements on the centerline of the jet show that turbulence remains constant at the level of the exit for a length, L_CT, which increases from L_CT = H at Re = 35,300 to L_CT = 4–5H at Re = 2200. The PIV measurements show that velocity remains constant at the exit level for a length, L_U, which increases from L_U = H at Re = 35,300 to L_U = 6H at Re = 2200 and is called undisturbed region of flow. In turbulent flow the length L_U is almost equal to the lengths of the regions of constant height, L_CH, and constant turbulence, L_CT. In laminar flow, Re = 2200, the length of the undisturbed region of flow, L_U, is greater than the lengths of the regions of constant height and turbulence, L_CT = L_CH = 4–5H. The average PIV and HFA velocity measurements confirm that the length of potential core, L_P, increases from L_P = 4–5H at Re = 35,300 to L_P = 7–8H at Re = 2200, and are compared to the previous experimental and theoretical results of the literature in the zone of mixing fluid and in the fully developed region with a good agreement.     

Hydrodynamic forces on a rotating sphere

The wake dynamics of a rotating sphere with prescribed rotation axis angles are quantitatively analysed by carrying out numerical simulations at Reynolds numbers of Re = 100, 250 and 300, non-dimensional rotational rates Ω¹ = 0–1 and rotation axis angles α = 0, π/6, π/3 and π/2 measured from the free stream axis. These parameters are the same as those in an earlier study (Poon et al., 2010, Int. J. Heat Fluid Flow) where the instantaneous flow structures were discussed qualitatively. This study extends the findings of the earlier study by employing phase diagrams (C_Lx, C_Ly) and (C_D, C_L) to provide a quantitative analysis of the time-dependent behaviour of the flow structures. At Re = 300 and Ω¹ = 0.05, the phase diagrams (C_Lx, C_Ly) show ‘saw tooth’ patterns for both α = 0 and π/6. The ‘saw tooth’ pattern indicates that the flow structures comprise a higher frequency oscillation component at a Reynolds number of 300 which is not observed until Re ≈ 800 for a stationary sphere. This ‘saw tooth’ pattern disappears as Ω¹ increases. The employment of the phase diagrams also reveals that different flow structures induce different oscillation amplitudes on both lateral force coefficients. With the exception of the vortices formed from a shear layer instability, all other flow regimes show larger fluctuations in C_L than C_D.     

Structure of the turbulent boundary layer over a rod-roughened wall

Turbulent coherent structures near a rod-roughened wall are scrutinized by analyzing instantaneous flow fields obtained from direct numerical simulations (DNSs) of a turbulent boundary layer (TBL). The roughness elements used are periodically arranged two-dimensional spanwise rods, and the roughness height is k/δ = 0.05 where δ is the boundary layer thickness. The Reynolds number based on the momentum thickness is varied in the range Re_θ = 300–1400. The effect of surface roughness is examined by comparing the characteristics of the TBLs over smooth and rough walls. Although introduction of roughness elements onto the smooth wall affects the Reynolds stresses throughout the entire boundary layer when scaled by the friction velocity, the roughness has little effect on the vorticity fluctuations in the outer layer. Pressure-strain tensors of the transport equation for the Reynolds stresses and quadrant analysis disclose that the redistribution of turbulent kinetic energy of the rough wall is similar to that of the smooth wall, and that the roughness has little effect on the relative contributions of ejection and sweep motions in the outer layer. To elucidate the modifications of the near-wall vortical structure induced by surface roughness, we used two-point correlations, joint weighted probability density function, and linear stochastic estimation. Finally, we demonstrate the existence of coherent structures in the instantaneous flow field over the rod-roughened surface.     

DNS and LES of turbulent flow in a closed channel featuring a pattern of hemispherical roughness elements

Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES) were performed for fully-developed turbulent flow in channels with smooth walls and walls featuring hemispherical roughness elements at shear Reynolds numbers Re_τ = 180 and 400, with the goal of studying the effect of these roughness elements on the wall-layer structure and on the friction factor. The LES and DNS approaches were verified first by comparison with existing DNS databases for smooth walls. Then, a parametric study for the hemispherical roughness elements was conducted, including the effects of shear Reynolds number, normalized roughness height (k⁺ = 10–20) and relative roughness spacing (s⁺/k⁺ = 2–6). The sensitivity study also included the effect of distribution pattern (regular square lattice vs. random pattern) of the roughness elements on the walls. The hemispherical roughness elements generate turbulence, thus increasing the friction factor with respect to the smooth-wall case, and causing a downward shift in the mean velocity profiles. The simulations revealed that the friction factor decreases with increasing Reynolds number and roughness spacing, and increases strongly with increasing roughness height. The effect of random element distribution on friction factor and mean velocities is however weak. In all cases, there is a clear cut between the inner layer near the wall, which is affected by the presence of the roughness elements, and the outer layer, which remains relatively unaffected. The study reveals that the presence of roughness elements of this shape promotes locally the instantaneous flow motion in the lateral direction in the wall layer, causing a transfer of energy from the streamwise Reynolds stress to the lateral component. The study indicates also that the coherent structures developing in the wall layer are rather similar to the smooth case but are lifted up by almost a constant wall-unit shift y⁺ (∼10–15), which, interestingly, corresponds to the relative roughness k⁺ = 10.     

The effect of sidewalls on rectangular jets

An experimental study is presented regarding the influence of sidewalls on the turbulent free jet flow issuing from a smoothly contracting rectangular nozzle of aspect ratio 15. “Sidewalls” are two parallel plates, flush with each of the slots’ short sides, practically establishing bounding walls extending the nozzle sidewalls in the downstream direction. Measurements of the streamwise and lateral velocity mean and turbulent characteristics have been accomplished, with an x-sensor hot wire anemometer, up to an axial distance of 35 nozzle widths, for jets with identical inlet conditions with and without sidewalls. Centreline measurements for both configurations have been collected for three Reynolds numbers, Re_D = 10,000, 20,000 and 30,000. For Re_D = 20,000 measurements in the transverse direction were collected at 13 different downstream locations in the range, x = 0–35 nozzle widths, and in the spanwise direction at three different downstream locations, x = 2, 6 and 25 nozzle widths.Results indicate that, the two jet configurations (with and without sidewalls) produce statistically different flow fields. Sidewalls do not lead to the production of a 2D flow field as undulations in the spanwise mean velocity distribution indicate. They do increase the two-dimensionality of the jet increasing the longevity of 2D spanwise rollers structures formed in the initial stages of entrainment, which are responsible for the convection of longitudinal momentum towards the outer field, establishing larger streamwise mean velocities at the jet edges. In the near field, up to 25 nozzle widths, lower outward lateral velocities in the presence of the sidewalls are held responsible for the decrease of turbulent terms including rms of velocity fluctuations and Reynolds stresses. Skewness factors increase monotonically across the shear layers from negative values to positive forming sharp peaks at the outer edges of the jet, illustrative of the presence of well defined 2D roller structures in the jet with sidewalls.     

Separated flow structures around a cylindrical obstacle in a narrow channel

A detailed experimental study is performed on the separated flow structures around a low aspect-ratio circular cylinder (pin-fin) in a practical configuration of liquid cooling channel. Distinctive features of the present arrangement are the confinement of the cylinder at both ends, water flow at low Reynolds numbers (Re = 800, 1800, 2800), very high core flow turbulence and undeveloped boundary layers at the position of the obstacle. The horseshoe vortex system at the junctions between the cylinder and the confining walls and the near wake region behind the obstacle are deeply investigated by means of Particle Image Velocimetry (PIV). Upstream of the cylinder, the horseshoe vortex system turns out to be perturbed by vorticity bursts from the incoming boundary layers, leading to aperiodical vortex oscillations at Re = 800 or to break-away and secondary vorticity eruptions at the higher Reynolds numbers. The flow structures in the near wake show a complex three-dimensional behaviour associated with a peculiar mechanism of spanwise mass transport. High levels of free-stream turbulence trigger an early instabilization of the shear layers and strong Bloor–Gerrard vortices are observed even at Re = 800. Coalescence of these vortices and intense spanwise flow inhibit the alternate primary vortex shedding for time periods whose length and frequency increase as the Reynolds number is reduced. The inhibition of alternate vortex shedding for long time periods is finally related to the very large wake characteristic lengths and to the low velocity fluctuations observed especially at the lowest Reynolds number.     

URANS of flow and endwall heat transfer in a pinned passage relevant to gas-turbine blade cooling

This paper presents some results of URANS study of flow and heat transfer in a matrix of wall-bounded 8 × 8 round pins, mimicking internal cooling passage of gas-turbine blades. The focus is on flow unsteadiness, its role in heat transfer and the capabilities of RANS models to reproduce these features in a set-up of industrial relevance. The results for two Reynolds numbers, 10 000 and 30 000, are compared with the available experiments and LES. It is shown that the elliptic-relaxation eddy-viscosity model, ζ-f captures vortex shedding and the consequent gross effects on the flow development. However, a closer look at flow details reveals discrepancies, especially around the first three pin rows, where the unsteadiness reproduced by URANS shows much weaker amplitudes as compared with LES. Only further downstream the succession of forcing from a series of pins produced unsteadiness akin to those captured by LES. The comparison suggests that smaller structures undetected by URANS need to be resolved to capture properly the separation and wake characteristics of each row. At Re = 10 000, the average endwall Nusselt number agrees well with the LES, both being about 20% lower than in the experiment. For Re = 30 000 the URANS Nusselt is within 10% of the experimental value.     

Hybrid RANS/LES computations of plane impinging jets with DES and PANS models

The qualities of a DES (Detached Eddy Simulation) and a PANS (Partially-Averaged Navier–Stokes) hybrid RANS/LES model, both based on the k–ω RANS turbulence model of Wilcox (2008, “Formulation of the k–ω turbulence model revisited” AIAA J., 46: 2823–2838), are analysed for simulation of plane impinging jets at a high nozzle-plate distance (H/B = 10, Re = 13,500; H is nozzle-plate distance, B is slot width; Reynolds number based on slot width and maximum velocity at nozzle exit) and a low nozzle-plate distance (H/B = 4, Re = 20,000). The mean velocity field, fluctuating velocity components, Reynolds stresses and skin friction at the impingement plate are compared with experimental data and LES (Large Eddy Simulation) results. The k–ω DES model is a double substitution type, following Davidson and Peng (2003, “Hybrid LES–RANS modelling: a one-equation SGS model combined with a k–ω model for predicting recirculating flows” Int. J. Numer. Meth. Fluids, 43: 1003–1018). This means that the turbulent length scale is replaced by the grid size in the destruction term of the k-equation and in the eddy viscosity formula. The k–ω PANS model is derived following Girimaji (2006, “Partially-Averaged Navier–Stokes model for turbulence: a Reynolds-Averaged Navier–Stokes to Direct Numerical Simulation bridging method” J. Appl. Mech., 73: 413–421). The turbulent length scale in the PANS model is constructed from the total turbulent kinetic energy and the sub-filter dissipation rate. Both hybrid models change between RANS (Reynolds-Averaged Navier–Stokes) and LES based on the cube root of the cell volume. The hybrid techniques, in contrast to RANS, are able to reproduce the turbulent flow dynamics in the shear layers of the impacting jet. The change from RANS to LES is much slower however for the PANS model than for the DES model on fine enough grids. This delays the break-up process of the vortices generated in the shear layers with as a consequence that the DES model produces better results than the PANS model.     

Direct numerical simulation of a NACA0012 in full stall

This work aims at investigating the mechanisms of separation and the transition to turbulence in the separated shear-layer of aerodynamic profiles, while at the same time to gain insight into coherent structures formed in the separated zone at low-to-moderate Reynolds numbers. To do this, direct numerical simulations of the flow past a NACA0012 airfoil at Reynolds numbers Re = 50,000 (based on the free-stream velocity and the airfoil chord) and angles of attack AOA = 9.25° and AOA = 12° have been carried out. At low-to-moderate Reynolds numbers, NACA0012 exhibits a combination of leading-edge/trailing-edge stall which causes the massive separation of the flow on the suction side of the airfoil. The initially laminar shear layer undergoes transition to turbulence and vortices formed are shed forming a von Kármán like vortex street in the airfoil wake. The main characteristics of this flow together with its main features, including power spectra of a set of selected monitoring probes at different positions on the suction side and in the wake of the airfoil are provided and discussed in detail.     

Flow structures around an equilateral triangle arrangement of three spheres

This paper represents the results of an experimental study on the flow structure around a single sphere and three spheres in an equilateral-triangular arrangement. Flow field measurements were performed using a Particle Image Velocimetry (PIV) technique and dye visualization in an open water channel for a Reynolds number of Re = 5 × 10³ based on the sphere diameter. The distributions and flow features at the critical locations of the contours of the velocity fluctuations, the patterns of sectional streamlines, the vorticity contours, the turbulent kinetic energy, the Reynolds stress correlations and shedding frequency are discussed. The gap ratios (G/D) of the three spheres were varied in the range of 1.0 ⩽ G/D ⩽ 2.5 where G was the distance between the sphere centers, and D was the sphere diameter which was taken as 30 mm. Due to the interference of the shedding shear layers and the wakes, more complex features of the flow patterns can be found in the wake region of the two downstream spheres behind the leading sphere. For G/D = 1.25, a jet-like flow around the leading sphere through the gap between the two downstream spheres occurred, which significantly enhanced the wake region. It was observed that a continuous flow development involving shearing phenomena and the interactions of shedding vortices caused a high rate of fluctuations over the whole flow field although most of the time-averaged flow patterns were almost symmetric about the two downstream spheres.     

LES of turbulent jet in cross-flow: Part 1 – A numerical validation study

The paper presents results of a LES based numerical simulation of the turbulent jet-in-cross-flow (JICF) flowfield, with Reynolds number based on cross-flow velocity and jet diameter Re = 2400 and jet-to-cross-flow velocity ratio of R = 3.3. The JICF flow case has been investigated in great detail, involving conduction of two independent precursor simulations, prior to the main JICF simulation, as the considered case has turbulent inflow conditions on both jet and cross-stream side. The LES results are directly compared to pointwise Laser Doppler Anemometry (LDA) measurements, showing a very good agreement on the level of various statistical quantities in all flow regions but the immediate jet-to-cross-flow exhaustion zone. Several LES computations involving grids of up to 15 million grid points have been conducted, showing no improvement in the agreement between numerical results and measurements, possibly indicating a LDA measurement problem in this particular region.     

Influence of wall proximity on characteristics of wake behind a square cylinder: PIV measurements and POD analysis

Influence of wall proximity on characteristics of the wake behind a two-dimensional square cylinder was experimentally studied in the present work. A low-speed recirculation water channel was established for the experiment; the Reynolds number based on the free-stream velocity and cylinder width (D) was kept at Re_D = 2250. Four cases with different gap width, e.g., G/D = 0.1, 0.2, 0.4 and 0.8, were chosen for comparison. Two experimental techniques, e.g., the standard PIV with high image-density CCD camera and TR-PIV with a high-speed camera were employed in measuring the wake field, enabling a comprehensive view of the time-averaged wake pattern at high spatial resolution and the instantaneous flow field at high temporal resolution, respectively. For the four cases, the difference in spatial characteristics of the wake in the vicinity of the plane wall was analyzed in terms of the time-averaged quantities measured by the standard PIV, e.g., the streamline pattern, the vector field, the streamwise velocity fluctuation intensity and the reverse-flow intermittency. The proper orthogonal decomposition (POD) method was extensively used to decompose the TR-PIV measurements, giving a close-up view of the energetic POD modes buried in the wake. The low-order flow model of the wake at G/D = 0.8 and 0.4 was constructed by using the linear combination of the first two POD modes and the time-mean flow field, which reflected well the vortex shedding process in the sense of the phase-dependent patterns. The intermittent appearance of the weakly separated region near the wall was found at G/D = 0.4. On going from G/D = 0.8 to 0.4, the remarkable variation of the instantaneous wake in the longitudinal direction confirmed that the wall constraint stretches the vortices in the plane of the wall and transfers the energy to the longitudinal component at the expense of the lateral one.     

Use of zero-net-mass-flow for separation control in diffusing S-duct

Flow control using zero-net-mass-flow jets in an S-shaped diffusing duct was investigated. Experiments were conducted in a channel flow facility at a Reynolds number, Re = 4.1 × 10⁴ with particle image velocimetry measurements in the symmetry plane of the duct. In the natural configuration, separation of the boundary layer occurs in a region of the duct with an high degree of curvature. A stability analysis of the wall normal base flow at the location of the applied control is presented and estimates the most effective frequency of the actuator. Time-averaged velocity fields show total reattachment of the boundary layer using active flow control.     

LES of the flow around several cuboids in a row

This paper presents Large Eddy Simulations (LES) of flow around a four-vehicle platoon when one of the platoon members was forced to undergo in-line oscillations. The LES were made at the Reynolds number of 10⁵ based on the height of the vehicles. Combinations of two different frequencies corresponding to non-dimensional frequencies at the Strouhal numbers St₁ = 0.025 and St₂ = 0.013 and two oscillation amplitudes were used in this study. The methodology was validated by comparisons with data from previous experimental investigations. In order to highlight the dynamic effects, comparisons were made with steady results on a single vehicle and on a four-vehicle platoon. Large differences were found in the flow structures between quasi-steady and dynamic results. Furthermore, the behavior of the drag coefficient of the upstream neighbor of the oscillating model was investigated.     

The flow field around a micropillar confined in a microchannel

The flow field over a low aspect ratio (AR) circular pillar (L/D = 1.5) in a microchannel was studied experimentally. Microparticle image velocimetry (μPIV) was employed to quantify flow parameters such as flow field, spanwise vorticity, and turbulent kinetic energy (TKE) in the microchannel. Flow regimes of cylinder-diameter-based Reynolds number at 100 ⩽ Re_D ⩽ 700 (i.e., steady, transition from quasi-steady to unsteady, and unsteady flow) were elucidated at the microscale. In addition, active flow control (AFC), via a steady control jet (issued from the pillar itself in the downstream direction), was implemented to induce favorable disturbances to the flow in order to alter the flow field, promote turbulence, and increase mixing. Together with passive flow control (i.e., a circular pillar), turbulent kinetic energy was significantly increased in a controllable manner throughout the flow field.