Lift Fluctuations Research Articles

Effect of variable pitch on flow around a helically twisted elliptic cylinder

We propose a new geometric disturbance called a variable pitch helically twisted elliptical (VPHTE) cylinder that was obtained by combining helically twisted elliptic (HTE) and asymmetric geometries for passive flow control. We confirmed that the new geometric disturbance reduces the drag and lift fluctuations compared with the smooth and HTE cylinders at the Reynolds number (Re) of 3000. Large eddy simulation was used for the evaluation of the flow control performance of the VPHTE cylinder at Re = 3000, which corresponds to the subcritical regime. A parametric study was conducted on the variable pitch ratio (VP). The smallest value of the time-averaged drag coefficient of the VPHTE cylinder is lower by about 16.7% and 4.1% than those of the smooth and HTE cylinders, respectively. Furthermore, a VPHTE cylinder reduces the root-mean-square value of the lift coefficient by 96.2% compared with a smooth cylinder. The vortex formation length related to the stabilization of the shear layer of the VPHTE cylinders is longer than those of the smooth and HTE cylinders, and it is consistently elongated as the VP increases. In addition, time-averaged pressure coefficients for different cylinders were compared to analyze the reason for the drag reduction. We systematically investigated the additional flow control performance of the VPHTE cylinders and VP effects by analyzing physical values such as the swirl strength, turbulent kinetic energy, and vorticity components around the VPHTE cylinders.

Effect of the geometric features of the harbor seal vibrissa based biomimetic cylinder on the forced convection heat transfer

The present study numerically investigates the effect of the geometrical features of a harbor seal vibrissa (HSV) on the forced convection heat transfer for the Reynolds number (Re) of 500 by using the large eddy simulation (LES). Seven HSV-like geometries are designed by combining the minor-axis undulation, the major-axis undulation, the both-axis undulation and the offset angle. In addition, the elliptic cylinder was included for the purpose of the comparison. All modified geometries with the HSV features present the reduction of the time-averaged drag coefficient, comparing to the mean drag coefficient of the elliptic cylinder. The geometries containing the major-axis undulation without an offset angle achieve a large amount of the reduction of the mean drag coefficient and the suppression of the lift fluctuation. The minor-axis undulation gives the smallest reduction of the drag coefficient and the lift fluctuation. The both-axis undulation produces the largest reduction rate of the time- and total surface-averaged Nusselt number in comparison with the elliptic cylinder. The undulation of the major-axis gives a larger effect on the spanwise dependence of the mean Nusselt number than that of the minor-axis. The presence of the wake vortices according to the spanwise position depend on the geometric features of the HSV, which associates to the thickness of the thermal boundary layer and eventually the heat transfer. It can be carefully concluded that the major-axis undulation among the geometric features of HSV is a key feature to affect the forced convection heat transfer.

Numerical investigation on the evolution of forces and energy features in thermo-sensitive cavitating flow

This study aims to investigate the evolution of transient force and energy features in a thermo-sensitive cavitating flow around a hydrofoil. A cavitation model is extended to investigate the thermal effect, and a shear stress transfer — partially averaged Navier–Stokes turbulence model is adopted to simulate the cavitating turbulent flow. The distribution of changed cavitation number is consistent with the cavity shape. The evident temperature gradient exists in the vicinity of the closure line, which leads the temperature drop to increasing gradually from the closure line to the centre of the cavity. The changed cavitation number also increases according to this rule. The force element analysis reveals that vortex structures induced by cavity evolution make the lift and drag forces fluctuation. Lift and drag forces increase approximately linearly with the development of sheet cavity. When the large attached sheet cavity separates from the suction surface, the lift and drag forces increase substantially. Conversely, the collapse of cloud cavity causes a sudden reduction of lift and drag forces. About the detailed evolution mechanisms of lift and drag forces, this work also expounds. Moreover, the terms in the kinetic energy transport equation are applied to depict the dissipation and transitivity of energy. The attached sheet cavity suppresses energy dissipation because of the stable flow field. The separation of sheet cavity and the shedding of cloud cavity induce the generation of multiscale vortex structures, and causes the energy loss to increase obviously. Combined with the analysis of the lift and drag forces, the evolution of fluid forces on the hydrofoil is also related to the energy loss.

Spanwise modulation of a three-dimensional wake using distributed forcing

Synthetic jets that are spatially distributed in the spanwise direction are used to control the flow over a circular cylinder. The Reynolds number based on the cylinder diameter and the free-stream velocity is Re = 500. To reveal how the finite spanwise forcing is coupled with the flow around the cylinder, three spanwise forcing wavelengths are considered, namely one, two, and three times of the cylinder diameter. Through distributed control, both the morphologic and dynamic features of the near wake are changed. The vortex shedding mode downstream of the forcing section can be converted from the original asymmetric form to a symmetric form, whereas the wake downstream of the no-forcing section is less influenced by the synthetic jets. Thus, the near-wake patterns and vortex dynamics vary in the spanwise direction according to the distributed forcing. In particular, the original large-scale Kármán vortex and streamwise vortex become smaller-scale vortices, and their spanwise characteristic length scale resembles the distributed forcing wavelength. This spanwise modulation by the proposed control strategy demonstrates that the lift fluctuations could be suppressed and the mean drag could be reduced, though this will be affected by the spanwise forcing wavelength.

Parallel vortex body interaction enabled by active flow control

An experimental investigation has been conducted to demonstrate the utility of active flow control as a disturbance generator for vortex body interaction studies. The technique is used to explore the flow physics of parallel vortex body interaction between two NACA 0012 airfoils in series. Experiments were carried out at a chord-based Reynolds number of 740,000 relative to the first airfoil. Active flow control in the form of nanosecond pulse-driven dielectric barrier discharge plasma actuation, originating close to the leading edge, was used to produce vortex shedding from the upstream (disturbance) airfoil at various frequencies ($$0.038 \le F^+ \le 0.762$$). These vortices were characterized, showing reduced circulation and diameter with increasing frequency, before examining the downstream wake-airfoil interactions. Time-resolved pressure and phase-locked PIV measurements were taken on the downstream (target) airfoil for multiple angles of attack. For $$F^+ \le 0.5$$, the target airfoil is subject to strong oscillations from the wake of the disturbance airfoil that lead to large fluctuations in lift and pitching moment. However, a further increase in $$F^+$$ reattaches the flow over the disturbance airfoil and no major vortex body interactions are observed on the target. Governing parameters for this type of vortex body interaction are explored, and differences between isolated and non-isolated encounters as well as the presence of a viscous response are examined. Finally, means to alleviate loads caused by the incident vortex are explored.

Robust active flow control over a range of Reynolds numbers using an artificial neural network trained through deep reinforcement learning

This paper focuses on the active flow control of a computational fluid dynamics simulation over a range of Reynolds numbers using deep reinforcement learning (DRL). More precisely, the proximal policy optimization (PPO) method is used to control the mass flow rate of four synthetic jets symmetrically located on the upper and lower sides of a cylinder immersed in a two-dimensional flow domain. The learning environment supports four flow configurations with Reynolds numbers 100, 200, 300, and 400, respectively. A new smoothing interpolation function is proposed to help the PPO algorithm learn to set continuous actions, which is of great importance to effectively suppress problematic jumps in lift and allow a better convergence for the training process. It is shown that the DRL controller is able to significantly reduce the lift and drag fluctuations and actively reduce the drag by ∼5.7%, 21.6%, 32.7%, and 38.7%, at Re = 100, 200, 300, and 400, respectively. More importantly, it can also effectively reduce drag for any previously unseen value of the Reynolds number between 60 and 400. This highlights the generalization ability of deep neural networks and is an important milestone toward the development of practical applications of DRL to active flow control.

Shear-induced viscosity stratified flow past a pair of heated side-by-side square cylinders in a confined domain

In this article, investigations have been carried out to decipher the effect of thermal buoyancy in a viscosity stratified flow field for a shear-thinning fluid flowing past a pair of heated side-by-side square cylinders, which is an extension part of our recent study [Sanyal, A. and Dhiman, A., “Wake interactions in a fluid flow past a pair of side-by-side square cylinders in presence of mixed convection,” Phys. Fluids 29, 103602 (2017)]. It is found that the leading-edge flow-separations from the square cylinders influence the near-wake structures and vortex shedding patterns in the presence of shear-thinning effects, which is otherwise missing for Newtonian fluid flow at Reynolds number Re = 40 and Richardson number Ri = 1. The distribution of wall-viscosity η along the inner surfaces of the side-by-side square cylinders, at different values of transverse spacings s/d and flow-behavior indices n, hints at large dependency on the inflections in the velocity profile within the gap-flow region. Under thermal buoyancy-driven mild shear-thinning flow conditions (n = 0.6 and 0.8), the gap-flow characteristics have been classified into “pressure-driven” and “momentum-driven” flow regimes, which provides a good explanation for the aberrations noted in the distribution pattern of η. The root-mean-square fluctuations of the velocity-magnitude and vortex shedding phenomenon are found to reciprocate a consistent flow physics associated with a shear-thinning flow at near and far-field downstream. The single body deflected type flow is primarily seen under predominant shear-thinning flow conditions (n = 0.4), compared to chaotic or quasi-periodic flow under mild shear-thinning conditions. Besides, the evolution of non-linear dynamics-based flow regimes (classified with respect to s/d using power spectrum density analysis) at different values of n and s/d is thoroughly summarized. The time-variant fluctuations of lift and drag force parameters are also found to be unified through cause and effects.

Heat transfer in magnetohydrodynamic nanofluid flow past a circular cylinder

Multi-phase modeling considering the nanofluid heterogeneity and slip velocity is not explored in simulating nanofluid flow and heat transfer at higher Reynolds numbers (Re). A comprehensive study of turbulent flow around hot circular cylinders is lacking. The flow patterns are not tackled, and the relationship between flow behaviors and force variations due to the influencing parameters is not established. The heat transfer enhancement and hydrodynamics with forced convection in a rectangular duct are investigated using Ansys FLUENT 15.0, applying a nodal spectral-element method based on the Eulerian-mixture model. The current investigation focuses on demonstrating the correlation between high Re values, size of the bluff body in relation to duct height, nanoparticle volume fraction, magnetic field strength, and heat transfer for magnetohydrodynamic flow. In general, the Nusselt number (Nu) increases with Re, cylinder diameter in relation to duct height, and nanoparticle volume fraction (ϕ) and decreases with the Hartmann number (Ha), except at Ha 0 ≤ 20. Nu increases with Ha from 0 to 20 with a drastic increase up to Ha = 10 and moderate from 10 to 20 with augment of Ha. The best heat transfer enhancement case is reported with the identification of ideal influencing parameters. The significant finding is that the control of flow over a circular cylinder for heat transfer enhancement using different parameters significantly changes vortical structures in the wake and reduces mean drag and lift fluctuations, destabilizes the shear layer and reattaches the flow on the surface before main separation, which delays main separation and decreases drag, and finally reduces the lift fluctuations.

Numerical study on the effect of damaged windows on aerodynamic characteristics of passenger trains under strong crosswind

Sand and gravel blown up by strong wind will cause damage to windows. Following up, it will cause the change in the flow field around a train immediately, which has a significant impact on the aerodynamic performance of the train. Delayed detached-eddy simulation based on the shear stress transport κ-ω turbulence model was used to investigate the aerodynamic characteristics of passenger vehicles under crosswind, and the effect of damaged windows on the train aerodynamic performance and flow field around the train was analyzed and compared. The grid generation and numerical method are verified in the previous studies. Results show that the aerodynamic performance of a passenger vehicle is significantly affected by damaged windows on both sides of the passenger vehicle, both the aerodynamic lateral force and overturning moment of the passenger vehicle were decreased, and this has a small effect on the aerodynamic performance of the downstream passenger vehicle. Fluctuation of the aerodynamic lift, lateral force, and overturning moment of a vehicle with damaged windows on both sides of the vehicle is significantly increased. Damaged windows do not change the existence of the main vortices around vehicles, but the size, location, and strength of the main vortices are obviously changed, especially when windows on both sides of the vehicle are damaged. Therefore, when windows on the windward side of the vehicles are damaged, opening or broking windows on the leeward side of the vehicles will help reduce the risk of vehicles overturning and derailment.

Suppression of vortex-induced vibration of a circular cylinder by a passive-jet flow control

In this study, vortex-induced vibrations (VIVs) of a spring system-supported circular cylinder model are suppressed via passive-jet flow control in wind tunnel experiments. A laser displacement measurement system is employed to obtain the vibration response of the test model with and without a passive-jet control scheme. The results indicate that the VIV oscillation amplitudes and frequency lock-in ranges of the controlled models are smaller than those of the baseline case. In addition to the vibration measurements, the pressure distribution in the test model is measured with a digital pressure measurement system. According to the surface pressure results, the mean pressures of the leeward surface are lifted, and the root-mean-square (RMS) pressures on the cylinder surface are suppressed compared with those of the baseline case. Moreover, in the controlled cases, the mean drag and lift fluctuations are remarkably alleviated, and the Reynolds shear stress in the cylinder wake decreases considerably. All results indicate that the effectiveness of the passive-jet flow control in this investigation is determined by the spacing of two neighboring jet pipes. Moreover, a linear correlation analysis of the surface pressures reveals that the correlation of the external surface pressure is tremendously disturbed by the passive-jet flow control.

Flow-induced vibration of a circular cylinder with splitter plates placed upstream and downstream individually and simultaneously

Flow-induced vibration (FIV) of a circular cylinder with splitter plates placed upstream and downstream individually and simultaneously at a low Reynolds number of 120 is numerically investigated using the direct numerical simulation (DNS). The effects of the downstream plate length and the arrangement of plates on the hydrodynamic forces, vibration response and flow wake are examined. The numerical results reveal that a downstream plate alleviates the vortex-induced vibration (VIV) at Ur≤9 (Ur is the reduced velocity) while exciting the galloping at Ur>9. The reattachment of shear layers on the plate surface generates an extra lift force, contributing to the galloping. The longer the plate, the larger the onset reduced velocity of galloping, which is associated with the jump of vibration amplitude and lift fluctuation as well as the fall of frequencies of vibration and vortex shedding. With the introduction of an upstream plate, the boundary layers develop along the plate before attaching on the cylinder surface, while the vortex shedding is delayed and flow wake is narrowed as compared to the bare cylinder, contributing to the VIV suppression. The galloping excited by the rear plate is eliminated by simultaneously placing an upstream plate, and the best suppression of VIV is achieved by the bilateral plates due to the more streamlined profile.

Dynamics of two-dimensional flow around a circular cylinder with flexible filaments attached.

A direction adaptive approach for the reduction of drag and the suppression of lift fluctuation in flow passing a circular cylinder is developed. Flexible filaments are attached to the surface of the cylinder, and different configurations, including the number, lengths, and angles of attachment of the filaments, as well as their tension and bending features, are investigated. In this comprehensive numerical study, the configuration with two filaments 180^{o} apart is found to be optimal for drag reduction and lift fluctuation suppression and is adaptive to the direction of the incoming flow. A drag reduction of 10.8% and a lift fluctuation suppression of 34.6% can be achieved as one filament is attached to the rear stagnation point and the other to the front stagnation point. The hairy coating resembled by 12 evenly attached filaments is also considered. Though marked drag reduction has not been found for this configuration, we leave it an open question for future studies to explore various properties of the filaments in turbulent flow, whose interaction with the filaments would be significant.

Direct numerical simulation of the wake adjustment and hydrodynamic characteristics of a circular cylinder symmetrically attached with fin-shaped strips

This work has numerically studied the effects of the coverage ratio and angular position of a pair of fin-shaped strips on the hydrodynamic forces and wake structures of a circular cylinder at both low and medium Reynolds numbers (Re = 60–500) using direct numerical simulation (DNS). The coverage ratio varies from 0.11 to 0.22, corresponding to the coverage angle (β) of a strip from 20° to 40°. The angular position (θ), measured from the forward stagnation point to the front edge of strips, ranges from 30° to 120° with increment of 30°. The numerical results indicate that the hydrodynamic coefficients are sensitive to the coverage and placement angles of the strips. The fluid forces are reduced with the introduction of a couple of 20°-fin-shaped strips, while they are amplified by placing 30°-fin-shaped strips or 40°-fin-shaped strips in the front surface of cylinder. The amplification/suppression is associated with the development of boundary layer and the wake structure, embodied in the length of recirculation bubble, the wake width, the tripping and reattachment of boundary layer as well as the separation point. By placing a pair of 40°-fin-shaped strips at θ = 60°, the time-mean drag and the lift fluctuation at Re = 180 are increased by 38.7% and 97.7%, respectively. For the cylinder equipped with 30°-fin-shaped strips at θ = 30°, the three-dimensional mode A and mode B wake structures are observed at medium Re = 200–500.

Double wavy geometric disturbance to the bluff body flow at a subcritical Reynolds number

A double wavy (DW) disturbance is newly proposed to obtain the reduction of drag and the fluctuating lift as the passive control for the bluff body flow. The present study expanded the asymmetry of Yoon et al. (2017) and combined two optimum wavelengths in the short and long wavelength ranges of Lam and Lin (2008) and Lin et al. (2016) to realize the DW geometric disturbance. Eventually, the flow past the DW cylinder was computed at the subcritical Reynolds number of 3000 using a large eddy simulation. The DW cylinder achieved the significant reduction of drag and fluctuating lift, compared to those of the smooth cylinder. It is noted that the DW cylinder achieved more reduction of drag and lift fluctuation than the wavy cylinder with the optimum wavelength. The DW cylinder formed the common characteristics of flow which associates with the reduction of drag and the fluctuating lift. The DW cylinder showed the double wavy profile of vortex formation length, which is due to the double wavy distribution of flow. Interestingly, the DW geometry gives a shorter wavy effect on the formation length. Namely, the saddle plane forms a longer formation length than the nodal plane.

Numerical Investigation of the Aerodynamic Characteristics and Attitude Stability of a Bio-Inspired Corrugated Airfoil for MAV or UAV Applications

In this study, two-dimensional (2D) and three-dimensional (3D) numerical calculations were conducted to investigate the aerodynamic characteristics, especially the unsteady aerodynamic characteristics and attitude stability of a bio-inspired corrugated airfoil compared with a smooth-surfaced airfoil (NACA2408 airfoil) at the chord Reynolds number of 4000 to explore the potential applications of non-traditional, corrugated dragonfly airfoils for micro air vehicles (MAVs) or micro-sized unmanned aerial vehicles (UAVs) designs. Two problem settings were applied to our numerical calculations. First, the airfoil was fixed at a constant angle of attack to analyze the aerodynamic characteristics and the hydrodynamic moment. Second, the angle of attack of airfoils was passively changed by the fluid force to analyze the attitude stability. The current numerical solver for the flow field around an unsteady rotating airfoil was validated against the published numerical data. It was confirmed that the corrugated airfoil performs (in terms of the lift-to-drag ratio) much better than the profiled NACA2408 airfoil at low Reynolds number R e = 4000 in low angle of attack range of 0 ∘ – 6 ∘ , and performs as well at the angle of attack of 6 ∘ or more. At these low angles of attack, the corrugated airfoil experiences an increase in the pressure drag and decrease in shear drag due to recirculation zones inside the cavities formed by the pleats. Furthermore, the increase in the lift for the corrugated airfoil is due to the negative pressure produced at the valleys. It was found that the lift and drag in the 2D numerical calculation are strong fluctuating at a high angle of attacks. However, in 3D simulation, especially for a 3D corrugated airfoil with unevenness in the spanwise direction, smaller fluctuations and the smaller average value in the lift and drag were obtained than the results in 2D calculations. It was found that a 3D wing with irregularities in the spanwise direction could promote three-dimensional flow and can suppress lift fluctuations even at high angles of attack. For the attitude stability, the corrugated airfoil is statically more unstable near the angle of attack of 0 ∘ , has a narrower static stable range of the angle of attack, and has a larger amplitude of fluctuations of the angle of attack compared with the profiled NACA2408 airfoil. Based on the Routh–Hurwitz stability criterion, it was confirmed that the control systems of the angle of attack passively changed by the fluid force for both two airfoils are unstable systems.

Passive separation control of a NACA0012 airfoil via a flexible flap

The incorporation of nature-inspired techniques to control or reduce boundary layer separation, to bring about performance enhancements on air/water vehicles, has been an active research area for many years. In this paper, a baseline NACA0012 airfoil is modified using a short flap on its upper surface at a Reynolds number of Re = 1000. The impact of the flap configuration—described by length, attachment position, deployment angle, and material properties, on the aerodynamic performance of the airfoil—quantified by mean and fluctuating forces, is investigated, and the flow field is analyzed. Inspired by the observation of pop-up feathers on a bird’s wing, the flap is first set to be rigid for a range of location, size, and inclination angles. After the optimal location of a rigid flap has been established, the flap is then allowed to be flexible, its motion is coupled to the encircling flow field, and it is tested for a range of mass ratios and bending stiffness values. The fluid motion is obtained by solving the lattice Boltzmann equation, while the dynamics of the flexible flap are calculated using the finite element method and the coupling between the flow and flap handled by the immersed boundary method. For the flexible flap, two flapping patterns are observed and the mechanism of separation control via rigid/flexible flap is explained. Compared to the flapless NACA0012 airfoil case, in the case with a flap of optimal configuration, the mean lift coefficient is improved by 13.51%, the mean drag coefficient is decreased by 3.67%, the mean lift-drag ratio is improved by 17.84%, the maximum lift fluctuation is decreased by 40.90%, and the maximum drag fluctuation is decreased by 56.90%.

Active Control of Bluff-Body Flows Using Plasma Actuators

Actuators play an important role in modern active flow control technology. Dielectric barrier discharge plasma can be used to induce localized velocity perturbations in air, so as to accomplish modifications to the global flow field. This paper presents a selective review of applications from the published literature with emphasis on interactions between plasma-induced perturbations and original unsteady fields of bluff-body flows. First, dielectric barrier discharge (DBD)-plasma actuator characteristics, and the local disturbance fields these actuators induce into the exterior flow, are described. Then, instabilities found in separated flows around bluff bodies that controlled actuation should target at are briefly presented. Key parameters for effective control are introduced using the nominally two-dimensional flow around a circular cylinder as a paradigm. The effects of the actuator configuration and location, amplitude and frequency of excitation, input waveform, as well as the phase difference between individual actuators are illustrated through examples classified based on symmetry properties. In general, symmetric excitation at frequencies higher than approximately five times the uncontrolled frequency of vortex shedding acts destructively on regular vortex shedding and can be safely employed for reducing the mean drag and lift fluctuations. Antisymmetric and symmetric excitation at low frequencies of the order of the natural frequency can amplify the wake instability and increase the mean and fluctuating aerodynamic forces, respectively, due to vortex locking-on to the excitation frequency or its subharmonics. Results from several studies show that the geometry and arrangement of the electrodes is of utmost significance. Power consumption is typically very low, but the electromechanical efficiency can be optimized by input waveform modulation.

Numerical experiments on using incline collar rings for controlling mean and fluctuating forces on circular bridge piers

This study was done to investigate the effects of angle and spacing of Collar-rings (innovative attachments for scour reduction over the circular piers) on the flow-induced forces on the circular piers. To this end, three angles (0°, 15°and 30°) and three relatives spacing (2/3, 3/3, and 4/3 of pier diameter) for the Collar-rings, have been considered. The ratio of the Collar-rings thickness to pier diameter was considered as 0.15. To compare the Collar-rings and helical cable performance, a circular pier with helical cable (the angle of 15°and the cable–pier diameter ratio of 0.15, suggested by previous experiments) is also numerically simulated. Reynolds number of the flow around circular piers with Collar-rings and helical cable is set to be 9554. In comparison to a plain surface pier, the results show that Collar-rings with the relative spacing of 4/3 for each three desired angles (0°, 15°and 30°) can reduce the mean and fluctuation of pressure, drag and lift coefficients around circular piers. Among tested configurations of the Collar-rings, Collar-rings with the relative spacing of 4/3 and angle of 15°are the best configuration to reduce the flow forces (mean pressure 5%, pressure fluctuation 24%, mean drag 2%, drag fluctuation 55%, fluctuation of lift 19%) around the simulated circular pier. Nevertheless, the helical cable increases flow forces (mean pressure 12%, pressure fluctuation 34%, mean drag 22%, drag fluctuation 110%, fluctuation of lift 30%). In addition to the flow forces and scour control around the circular piers, this tool can be readily and economically installed on the existing circular piers.

Large Eddy Simulation of Flow over Wavy Cylinders with Different Twisted Angles at a Subcritical Reynolds Number

The deformation of the cylinder has been proved to greatly reduce the fluctuation of lift and the vortex-induced vibration. In this article, a new form of deformation mode for the smooth cylinder is proposed in order to reduce the vortex-induced vibrations, which can be applied to marine risers and submarine pipelines to ensure the working performance and safety of offshore platforms. Large eddy simulation (LES) is adopted to simulate the turbulent flow over wavy cylinders with three different twisted angles at a subcritical Reynolds number Re = 28,712. Comparing with the results of smooth cylinder, the maximum drag and lift reduction of wavy cylinder A3 with α = 40° can reach 17% and 84%, respectively, and the corresponding vortex formation length increases significantly, while the turbulence intensity decreases relatively. Meanwhile, the circumferential minimum pressure coefficient is greater than that of the smooth cylinder, which also provides a greater drag reduction for the cylinder. The surface separation line, turbulent kinetic energy distribution, and wake vortex structure indicate that the elongation of separated shear layer and wake shedding position is larger than that of the smooth cylinder, and the vorticity value in the near wake region decreases. A periodic vortex structure is generated along the spanwise direction, and a weaker and more stable Karman vortex street is reformed at a further downstream position, which ultimately leads to the reduction of drag and fluctuating lift of the wavy cylinder.

Effect of a double wavy geometric disturbance on forced convection heat transfer at a subcritical Reynolds number

The present study initially considered the double wavy (DW) shape as the geometric disturbance to control fluid flow and the heat transfer. The large eddy simulation (LES) was performed to solve the filtered momentum and energy equations at the subcritical Reynolds number of 3000 and the Prandtl number of 0.7. In order to evaluate the effect of DW geometry on the force coefficients and the heat transfer, the smooth (CY), and symmetric wavy (SW) and asymmetric wavy (ASW) cylinders are considered for the purpose of the comparison. The DW cylinder achieved the smallest mean drag and the largest suppression of the lift fluctuation among the different geometric disturbances. The Nusselt number of the DW cylinder has the smallest mean and fluctuation values. The spanwise local Nusselt number is strongly correlated to the geometric disturbance, which is consistent with the SW and ASW cylinders. The DW cylinder provided smaller spanwise local Nusselt number over the span than the SW and ASW cylinders. The DW cylinder attenuates the heat transfer in comparison with the circular cylinder. The wake modification by the DW cylinder associates to the attenuation of the heat transfer.