Effect of tube spacing on the vortex shedding characteristics of laminar flow past an inline tube array: A numerical study

The effect of tube spacing on the vortex shedding characteristics and fluctuating forces in an inline cylinder array is studied numerically. The examined Reynolds number is 100 and the flow is laminar. The numerical methodology and the code employed to solve the Navier-Stokes and continuity equations in an unstructured finite volume grid are validated for the case of flow past two tandem cylinders at four spacings. Computations are then performed for a six-row inline tube bank for eight pitch-to-diameter ratios, s, ranging from 2.1 to 4. At the smallest spacing examined (s = 2.1) there are five stagnant and symmetric recirculation zones and weak vortex shedding activity occurs only behind the last cylinder. As s increases, the symmetry of the recirculation zones breaks leading to vortex shedding and this process progressively moves upstream, so that for s = 4 there is clear shedding from every row. For any given spacing, the shedding frequency behind each cylinder is the same. A critical spacing range between 3.0 and 3.6 is identified at which the mean drag as well as the rms lift and drag coefficients for the last three cylinders attain maximum values. Further increase to s = 4 leads to significant decrease in the force statistics and increase in the Strouhal number. It was found that at the critical spacing there is 180° phase difference in the shedding cycle between successive cylinders and the vortices travel a distance twice the tube spacing within one period of shedding.     

Large eddy simulation of pulsating flow over a circular cylinder at subcritical Reynolds number

The pulsating cross-flow over a single circular cylinder at the subcritical Reynolds number Re_D = 2580 is studied with the large eddy simulation (LES) technique using the standard Smagorinsky model as well as a dynamic model in which the test filtered quantities are evaluated through a truncated Taylor series expansion. The filtered equations are discretised using the finite volume method in an unstructured, collocated grid arrangement with a second-order accurate method, in both space and time. The predictions are compared against very detailed experiments for mean velocities and Reynolds stresses that were performed in a duct of cross-section 72 mm × 72 mm using the PIV technique. The effects of mesh refinement close to the cylinder as well as of subgrid scale model are also examined. The numerical predictions are in very good agreement with the measurements in terms of mean as well as turbulence quantities. The instantaneous flow patterns of the flow field are examined and the effect of the external flow pulsation on the wake characteristics such as vortex formation length, vortex strength, Strouhal number as well as the lift and drag coefficients is quantified. The vortex formation length is decreased while the mean drag, as well as the rms values of the drag and lift coefficients increase significantly under pulsating flow conditions. The performance of the LES technique is analysed in the light of the wake characteristics.     

Dynamic hybridization of MILES and RANS for predicting airfoil stall

Hybridization comprised of an algebraic turbulence model based on the Reynolds average Navier-Stokes (RANS) equations with a monotonically integrated large eddy simulation (MILES) is proposed to simulate transient fluid motion during separation and vortex shedding at high Reynolds numbers. The proposed hybridization utilizes the Baldwin-Lomax model with the Degani-Schiff modification as the RANS model in the near-wall region and a MILES far from the wall. Although the hybridization is assumed to be a MILES with wall modeling, the transition line between the RANS and the MILES modes is determined by the turbulent intensity that is dominated by the large eddies in the grid-scale. This hybrid model is applied to the flows past three different types of airfoils (NACA63₃-018, NACA63₁-012 and NACA64A-006) near stall, at a chord Reynolds number of Re = 5.8 × 10⁶. These airfoils are classified as trailing-edge-stall, leading-edge-stall and thin-airfoil-stall airfoils, respectively. The computed results are compared with wind tunnel experiments. The hybrid model successfully demonstrates accurate stall angle and surface pressure distribution predictions near the stall for each type of airfoil. The airfoil simulation results confirmed that the hybrid model provides a better prediction than the RANS model for unsteady turbulent flows with separation and vortex shedding simulations.     

DNS of a plane mixing layer for the investigation of sound generation mechanisms

Direct numerical simulations in two and three dimensions have been performed to investigate the sound generation by vortex pairing in a compressible plane mixing layer with Ma₁ = 0.5 being the upper and Ma₂ = 0.25 being the lower stream Mach number. The Reynolds number based on the vorticity thickness at the inflow and the velocity of the upper stream is Re=500. The flow is forced at the inflow with eigenfunctions obtained from viscous linear stability theory including three-dimensional disturbances. The results are verified with linear stability theory and the two-dimensional simulations performed by Colonius et al. [Colonius T, Lele SK, Moin P. Sound generation in a mixing layer. J Fluid Mech 1997;330:375-409]. The excitation of a steady longitudinal vortex mode leads to an early three-dimensional deformation of the travelling spanwise vortices and reduced sound emission to the slower fluid stream side.     

On wave harmonics of heated circular cylinders

A hybrid (FV + FE) acoustic damping method, which is investigated and optimized in terms of wave harmonics behavior of the method, is utilized at Ma = 0.01 for heated circular cylinders. Discretization of nonlinear convective terms is a modified approximate Riemann solver. Modification is realized through multiplication of dissipation term with an acoustic damping matrix. This is necessary to avoid drawbacks of standard algorithm and to improve accuracy of results, if low speed applications are concerned. Later, harmonics of velocity and temperature fields behind a heated circular cylinder are investigated numerically for moderate Reynolds numbers between 70 and 110. A parametric study of the first harmonics is carried out precisely by increasing temperature ratios, T^∗ = T_wall/T_∞ from 1.03 to 1.8. Results agree well for high temperature ratios, T^∗ = 1.5, 1.8 and Re ? 100, with the key issues stated in the experimental work of Ezersky et al. [Ezersky AB, Lecordier JC, Paranthoën P, Soustov PL, Structure of vortices in a Karman street behind a heated cylinder. Phys Rev E 2000;61:2107]. Moreover, it is found that decrease in frequency of oscillations can be explained as heated cylinders have larger vortex formation region as a result of heat flux from walls in comparison to non-heated cylinders. At lower temperature ratios, T^∗ = 1.03, 1.1, temperature can be taken as passive scalar field.     

Numerical simulation of flow past row of square cylinders for various separation ratios

A systematic study for the flow around a row of five square cylinders placed in a side-by-side arrangement and normal to the oncoming flow at a Reynolds number of 150 is carried out through the numerical solution of the two-dimensional unsteady incompressible Navier-Stokes equations. Special attention is paid to investigate the effect of the spacing between the five cylinders on the wake structure and vortex shedding mechanism. The simulations are performed for the separation ratios (spacing to size ratio) of 1.2, 2, 3 and 4. Depending on the separation ratio the following flow patterns are observed: a flip-flopping pattern, in-phase and anti-phase synchronized pattern and non-synchronized pattern. These flow patterns are supposed to be a consequence of the interaction between two types of frequencies viz. the vortex shedding (primary) and the cylinder interaction (secondary) frequencies. At small separation ratio the flow is predominantly characterized by the jet in the gaps between successive cylinders and the secondary frequencies play a role in the resulting chaotic flow. On the contrary, at higher separation ratio the secondary frequencies almost disappear and the resulting flow becomes more synchronized dominated by the primary frequency.     

Particle mixing and reactive front motion in unsteady open shallow flow - Modelled using singular value decomposition

Passive and active tracers are used to examine particle mixing and reactive front dynamics in an open shallow flow of water past a circular cylinder. A quadtree grid based Godunov-type shallow water equation solver predicts the unsteady flow hydrodynamics of the wake behind the cylinder. The resulting periodic flow field consisting of a von Kármán vortex street is decomposed and stored over one oscillatory period using Singular Value Decomposition (SVD). Particles are advected according to the reconstructed flow field from the SVD modes, with continuous spatial velocity information obtained via bilinear interpolation. Passive particle dynamics driven by different SVD flow modes is investigated, and it is found that the flow field recovered from the mean flow and the first pair of time varying modes is adequate to represent the complicated dynamical properties induced by the original flow field. Active autocatalytic reaction, A + B → 2B, is incorporated into the particle advection model, assuming surface reaction. Active particles are found to trace out an expanded version of the unstable manifold of the chaotic saddle in the wake, in qualitative agreement with published analytical results. The numerical model is applicable to mixing and transport processes in more complicated shallow environmental flows.     

Improvement of jitter transfer characteristics of a 9.95328 Gb/s data recovery DLL using saw filter

This paper presents a design of a high-speed data recovery circuit for non return zero (NRZ) data transmission using delay-locked loop (DLL) with SAW filter. The jitter generation of the circuit is decreased by adjusting the loop gain in DLL whereas surface acoustic wave (SAW) filter with low centered frequency (f_c) improves the jitter transfer function of DLL. It is seen that the circuit using SAW filter of f_c = 1.24416 GHz and Q = 1000 provides the cut off frequency of about 600 kHz which is ∼10 times lower than that of conventional DLL circuit.     

Frequency characteristics of coherent structures and their excitations in small aspect-ratio rectangular jets using large eddy simulation

Large eddy simulations of air jets from small aspect-ratio (AR) rectangular nozzles are performed with the dynamic subgrid-scale closure. Mean streamwise velocity profiles are in good agreement with experimental data. Results indicate that vortices originating from the longer side of the rectangular jet are dominant compared with that from the shorter side. Furthermore, entrainment is slight in the potential core, and significantly increases in the following vortex roll-up region. However, the jet entrains more with smaller AR. Power spectral density of the streamwise velocity indicates that the oscillations consist of a series of sub-harmonic frequencies, with the predominant frequencies reducing along the axial direction. Analysis shows that among multiple frequencies, there is a characteristic one at f = 0.22 which dominates the near field of the rectangular jet. The characteristic frequency is independent of velocity components, aspect ratios of the jet and locations. Based on this characteristic frequency, calculations with different forced frequencies imposed on the inlet nozzle are carried out. Results indicate that when the forced frequency is approximately equal to the characteristic frequency, development of the coherent structures is the most intense in the near field, and exhibits the strongest entrainment.     

Two-dimensional side-by-side circular cylinders at moderate Reynolds numbers

In a companion article [1], we described computer simulations of the flow around 2 two-dimensional, tandem circular cylinders in a flow for 1?Re?20. In this article we adopt a similar approach to characterize the flow around side-by-side cylinders with surface-to-surface separation/diameter in the range 0.1 < s/D < 30. The results revealed some distinct and interesting features of the flow, which are completely different than those observed at higher Reynolds numbers.At low Reynolds numbers, 1?Re?5, for all gap spacings, the flow contains no regions of flow separation. At higher Re, four distinct flow behaviors were observed. For very small gap spacings, e.g. 0.1 < s/D < 0.6 at Re = 20, two elongated “detached vortices” form downstream of the cylinders. The drag coefficient increases sharply with the gap spacing. For gap spacings 0.6 < s/D < 0.7 at Re = 20, no vortices form anywhere in the flow. For gap spacings around s/D ≈ 1 separation regions form only on the inside portions of the cylinders. For larger gap spacings s/D > 1 the flow reverts to something similar to that around an isolated cylinder in the flow, i.e. two attached vortices on the rear side of each cylinder. In general, the drag coefficient increases as the gap spacing increases. At higher Reynolds number it is known that the cylinder lift coefficients decrease monotonically with gap spacing. In contrast, at these lower Reynolds number the lift coefficient curves rise to a maximum for 0.3 < s/D < 3 and then decrease monotonically for larger s/D.     

Analysis and control of the near-wake flow over a square-back geometry

A 3D numerical simulation, based on the Lattice Boltzmann method is carried out on the near-wake flow behind a generic square-back blunt body to analyze and establish a method to control the near-wake flow. The flow topology is described by the velocity and the pressure fields. The influence of the wake vortices on the aerodynamic drag is clarified and quantified. In order to reduce this drag, an active open-loop flow control is applied by continuous blowing devices distributed around the base periphery. The blowing effect on the behind body flow is a reduction of the wake section and of the total pressure loss in the wake and an increase of the static pressure on the base of the square body. This control leads to a significant drag reduction of ΔC_x = −29% with a blowing velocity of 1.5V₀. The efficiency is then studied, and we found that the most efficient control is obtained for a blowing velocity of 0.5V₀ and a jet angle of 45°. In this case, a 20% drag reduction is obtained, and the energy needed to control the system is seven times lower than the energy saved by the control.     

Numerical prediction of unsteady vortex shedding for large leading-edge roughness

A full two-dimensional Navier-Stokes algorithm is used to investigate unsteady, incompressible viscous flow past an airfoil leading edge with surface roughness that is characteristic of ice accretion. The roughness is added to the surface through the use of a Prandtl transposition and can generate both small-scale and large-scale roughness. The focus of the study is a detailed flow analysis of the unsteady velocity fluctuations and vortex shedding induced by the surface roughness. The results of this study are compared to experimental data on roughness-induced transition for the same roughness geometry. A comparison is made between “fluctuation intensity” values from the current algorithm to experimentally determined turbulence intensity values. The effects of the roughness Reynolds number, Re_k, are investigated and compared to experimental values of the critical roughness Reynolds number. The authors speculate that there may be a possible correlation between unsteady roughness-induced vortex shedding and the onset of experimentally measured transitional flow downstream of large-scale roughness.     

Edge-bipancyclicity of the k-ary n-cubes with faulty nodes and edges

The k-ary n-cube has been one of the most popular interconnection networks for massively parallel systems. In this paper, we investigate the edge-bipancyclicity of k-ary n-cubes with faulty nodes and edges. It is proved that every healthy edge of the faulty k-ary n-cube with f_v faulty nodes and f_e faulty edges lies in a fault-free cycle of every even length from 4 to kⁿ − 2f_v (resp. kⁿ − f_v) if k ? 4 is even (resp. k ? 3 is odd) and f_v + f_e ? 2n − 3. The results are optimal with respect to the number of node and edge faults tolerated.     

Numerical modeling of interaction of a current with a circular cylinder near a rigid bed

The numerical modeling of 2D turbulent flow around a smooth horizontal circular cylinder near a rigid bed with gap ratio G/D = 0.3 at Reynolds number Re_D = 9500 is investigated. Ansys^® 10.0-FLOTRAN program package is used to solve the governing equations by FEM, and the performance of the standard k ? ε, standard k ? ω, and SST turbulence models are examined. A sensitivity study for the three turbulence models is carried out on three computational meshes with different densities near the cylinder surface. The computational velocity fields and the Strouhal numbers from the present simulations are compared with those obtained from the PIV measurement. It is found that the time-averaged velocity field of the flow in the proximity of the cylinder is closely affected by the mesh resolution near the cylinder surface, and the mesh refinement in radial direction improves the results of present simulations. The shedding of vortices in the cylinder wake is not predicted by k ? ε model on all the three meshes. The results for the time-averaged velocity field show that the numerical modeling using either of k ? ω and SST turbulence models on the finest mesh used on the cylinder surface is reasonably successful.     

A fibre-optic grating sensor for the study of flow-induced vibrations

A fibre-optic Bragg grating sensor for flow-induced vibration measurement is described. The sensor is based on monitoring shift in the Bragg wavelength of a fibre Bragg grating. The fibre Bragg grating, when bonded onto a structure, can measure local axial strain variation of the structure. The sensor was used to measure the flow-induced vibrations on a circular cylinder in a cross-flow. The measured strain ε is consistent with the transverse structural bending displacement Y obtained from a laser vibrometer in terms of the natural frequency of the fluid–structure system and the vortex shedding frequency. The experimental data further indicated that ε and Y are linearly correlated when the bending displacement is small. It is expected that the fibre Bragg grating sensor, because of its physical uniqueness, has an important role to play in the study of fluid–structure interactions.     

On embedding cycles into faulty twisted cubes

The twisted cube TQ_n is an alternative to the popular hypercube network. Recently, some interesting properties of TQ_n were investigated. In this paper, we study the pancycle problem on faulty twisted cubes. Let f_e and f_v be the numbers of faulty edges and faulty vertices in TQ_n, respectively. We show that, with f_e + f_v ? n − 2, a faulty TQ_n still contains a cycle of length l for every 4 ? l ? ∣V(TQ_n)∣ − f_v and odd integer n ? 3.     

Low-frequency noise in planar Hall effect bridge sensors

The low-frequency characteristics of planar Hall effect bridge sensors are investigated as function of the sensor bias current and the applied magnetic field. The noise spectra reveal a Johnson-like spectrum at high frequencies, and a 1/f-like excess noise spectrum at lower frequencies, with a knee frequency of around 400 Hz. The 1/f-like excess noise can be described by the phenomenological Hooge equation with a Hooge parameter of γ_H = 0.016. The detectivity is shown to depend on the total length, width and thickness of the bridge branches. The detectivity is improved by the square root of the length increase. Moreover, the detectivity is shown to depend on the amplitude of the applied magnetic field, revealing a magnetic origin to part of the 1/f noise.     

Large-eddy simulations of film cooling flows

Large-eddy simulations (LES) of a jet in a cross-flow (JICF) problem are carried out to investigate the turbulent flow structure and the vortex dynamics in gas turbine blade film cooling. A turbulent flat plate boundary layer at a Reynolds number of Re_∞ = 400,000 interacts with a jet issued from a pipe. To study the effect of the jet inclination angle α on the flow field, two angles are chosen, the perpendicular injection at 90° and the streamwise inclined injection at 30°. For the normal injection case a small blowing ratio of the jet velocity to the cross-stream velocity R = 0.1 is examined. For the streamwise inclined injection case two blowing ratios R = 0.1 and R = 0.48 are investigated to check the impact of the jet velocity on the cooling performance. The time-dependent turbulent inflow information for the cross-flow is provided by a simultaneously performed LES of a spatially developing turbulent boundary layer. Whereas in the perpendicular injection case a rather large separation region is found at the leading edge of the jet hole, in the streamwise inclined injection cases no separation is observed. Compared with the normal injection case at the same blowing ratio, the streamwise inclination weakens the jet-cross-flow interaction significantly. Thus, the first appearance of the counter-rotating vortex pair (CVP) is shifted downstream and its strength is reduced. The increase of the blowing ratio leads to a stronger penetration of the jet into the cross-flow, resulting in a more upstream located and more pronounced CVP. Downstream of the jet exit the streamwise vortices are so large that besides the jet fluid also the cross-stream is partially entrained into this zone, which yields the worst cooling performance.     

Wafer mapping of the transverse piezoelectric coefficient, e31,f, using the wafer flexure technique with sputter deposited Pt strain gauges

Measurement of the transverse piezoelectric coefficient (e_31,f) in thin films is crucial for the development of microfabricated sensors, actuators, and transducers. Here, a method is described such that lithographically defined strain gauges enable non-destructive, position-dependent characterization of e_31,f in conjunction with the wafer flexure technique. Measurements of 100 nm thick Pt gauges deposited on 1 μm thick PbZr_0.52Ti_0.48O₃ thin films yield gauge factors of 6.24, with a gauge-to-gauge variation that is 5% of this value. The system allows for simultaneous measurement of the charge and strain, improving the overall accuracy of measurement. The small footprint of the combined strain gauge array/electrode pattern used for determining e_31,f, allows for a non-destructive mapping of the transverse piezoelectric coefficient across large-area wafers. Due to the clamping configuration used in wafer flexure experiments, e_31,f values can accurately be obtained within the central ∼2/3 of a full wafer. Measurements performed on a 1.3 μm thick randomly oriented polycrystalline PbZr_0.52Ti_0.48O₃ film made deposited on a 4 in. platinized silicon wafer by the sol-gel process show a high degree of uniformity, with e_31,f of −6.37 ± 0.60 C/m² for points measured within r = 3 cm.     

Flow patterns past two circular cylinders in proximity

Flow patterns past two nearby circular cylinders of equal diameter immersed in the cross-flow at low Reynolds numbers (Re ? 160), were numerically studied using an immersed boundary method. We considered all possible arrangements of the two cylinders in terms of the distance between the two cylinders and the inclination angle of the line connecting the cylinder centers with respect to the direction of the main flow. Ten distinct flow patterns were identified in total based on vorticity contours and streamlines, which are Steady, Near-Steady, Base-Bleed, Biased-Base-Bleed, Shear-Layer-Reattachment, Induced-Separation, Vortex-Impingement, Flip-Flopping, Modulated Periodic, and Synchronized-Vortex-Shedding. Collecting all the numerical results obtained, we propose a general flow-pattern diagram for each Re, and a contour diagram on vortex-shedding frequency for each cylinder at Re = 100. The perfect symmetry implied in the geometrical configuration allows one to use these diagrams to identify flow pattern and vortex-shedding frequencies in the presence of two circular cylinders of equal diameter arbitrarily positioned in physical space with respect to the main-flow direction.