Bluff Body Flows Research Articles

Analysis of the cross-flow features around two side-by-side rectangular cylinders

This study employs the lattice Boltzmann method (LBM) to numerically analyze the fluid flow around two side-by-side rectangular cylinders with an aspect ratio (AR) of 3:2. The gap spacing (G) between the cylinders is taken in the range 0–10 and the Reynolds number (Re) is fixed at 200. The numerical outcomes depict a strong correlation between flow patterns, force variations, gap spacing, and aspect ratio. Among these parameters, the latter ones strongly influence the flow-induced drag, lift, and pressure. The mean drag coefficient (CDmean), Strouhal number (St), and root-mean-square values of force coefficients exhibit rapid variations under the impact of these parameters for both cylinders. The observed outcomes further indicate that flow structures in the wake vary with changes in gap spacing. Five separate patterns of wake flow are detected, depending on varying gap spacing. These patterns include isolated bluff-body flow, flip-flopping flow, non-synchronized flow, modulated synchronized flow, and synchronized flow.

Spacing effects on flows around two square cylinders in staggered arrangement via LBM

This study presents a computational analysis of fluid flow characteristics around two staggered arranged square cylinders using the Lattice Boltzmann Method (LBM). With Reynolds number (Re) fixed at 200, numerical simulations explore the influence of varying gap ratios (G) ranging from 0 to 10 times the cylinder size. Emphasis is placed on understanding the impact of cylinders spacing on flow structure mechanisms and induced forces. Investigation of fluid flow parameters includes vorticity behavior, pressure streamlines, and variations in drag and lift coefficients alongside the Strouhal number under different values of G. From the results, four distinct flow patterns emerge: single bluff body flow, flip flopping flow, modulated synchronized flow, and synchronized flow, each exhibiting unique characteristics. This study reveals the strong dependence of fluid forces on G, with low spacing values leading to complex vortex structures and fluctuating forces influenced by jet flow effects. At higher spacing values, proximity effects between cylinders diminish, resulting in a smoother periodic flow. The Strouhal number, average drag force and the rms values of drag and lift force coefficients vary abruptly at narrow gaps and become smooth at higher gap ratios. Unlike the tandem and side-by-side arrangements the staggered cylinders arrangement is found to have significant impact on the pressure variations around both cylinders. Overall, this research could contribute to a comprehensive understanding of staggered cylinder arrangements and their implications for engineering applications.

On the prediction of the turbulent flow behind cylinder arrays via echo state networks

This study aims at the prediction of the turbulent flow behind cylinder arrays by the application of Echo State Networks (ESN). Three different arrangements of arrays of seven cylinders are chosen for the current study. These represent different flow regimes: single bluff body flow, transient flow, and co-shedding flow. This allows the investigation of turbulent flows that fundamentally originate from wake flows yet exhibit highly diverse dynamics. The data is reduced by Proper Orthogonal Decomposition (POD) which is optimal in terms of kinetic energy. The Time Coefficients of the POD Modes (TCPM) are predicted by the ESN. The network architecture is optimized with respect to its three main hyperparameters, Input Scaling (INS), Spectral Radius (SR), and Leaking Rate (LR), in order to produce the best predictions in terms of Weighted Prediction Score (WPS), a metric leveling statistic and deterministic prediction. In general, the ESN is capable of imitating the complex dynamics of turbulent flows even for longer periods of several vortex shedding cycles. Furthermore, the mutual interdependencies of the TCPM are well preserved. However, optimal hyperparameters depend strongly on the flow characteristics. Generally, as flow dynamics become faster and more intermittent, larger LR and INS values result in better predictions, whereas less clear trends for SR are observable.

Deep reinforcement learning-based active flow control of an elliptical cylinder: Transitioning from an elliptical cylinder to a circular cylinder and a flat plate

We study the adaptability of deep reinforcement learning (DRL)-based active flow control (AFC) technology for bluff body flows with complex geometries. It is extended from a cylinder with an aspect ratio Ar = 1 to a flat elliptical cylinder with Ar = 2, slender elliptical cylinders with Ar less than 1, and a flat plate with Ar = 0. We utilize the Proximal Policy Optimization (PPO) algorithm to precisely control the mass flow rates of synthetic jets located on the upper and lower surfaces of a cylinder to achieve reduction in drag, minimization of lift, and suppression of vortex shedding. Our research findings indicate that, for elliptical cylinders with Ar between 1.75 and 0.75, the reduction in drag coefficient ranges from 0.9% to 15.7%, and the reduction in lift coefficient ranges from 95.2% to 99.7%. The DRL-based control strategy not only significantly reduces lift and drag, but also completely suppresses vortex shedding while using less than 1% of external excitation energy, demonstrating its efficiency and energy-saving capabilities. Additionally, for Ar from 0.5 to 0, the reduction in drag coefficient ranges from 26.9% to 43.6%, and the reduction in lift coefficient from 50.2% to 68.0%. This reflects the control strategy's significant reduction in both drag and lift coefficients, while also alleviating vortex shedding. The interaction and nonlinear development of vortices in the wake of elliptical cylinders lead to complex flow instability, and DRL-based AFC technology shows adaptability and potential in addressing flow control problems for this type of bluff body flow.

Exploring Vortex–Flame Interactions and Combustion Dynamics in Bluff Body-Stabilized Diffusion Flames: Effects of Incoming Flow Velocity and Oxygen Content

An afterburner encounters two primary features: high incoming flow velocity and low oxygen concentration in the incoming airflow, which pose substantial challenges and contribute significantly to the deterioration of combustion performance. In order to research the influence of oxygen content on the dynamic combustion characteristics of the afterburner under various inlet velocities, the effect of oxygen content (14–23%) on the field structure of reacting bluff body flow, flame morphology, temperature pulsation, and pressure pulsation of the afterburner at different incoming flow velocities (0.1–0.2 Ma) was investigated in this study by using a large eddy simulation method. The results show that two different instability features, BVK instability and KH instability, are observed in the separated shear layer and wake, and are influenced by changes in the O2 mass fraction and Mach number. The oxygen content and velocity affected the oscillation amplitude of the downstream flow. As the O2 mass fraction decreases, the flame oscillation amplitude increases, the OH concentration in the combustion chamber decreases, and the flame temperature decreases. Additionally, the amplitude of the temperature pulsation in the bluff body flame was primarily influenced by the temperature intensity of the flame and BVK instability. Moreover, the pressure pulsation is predominantly affected by the dynamic characteristics of the flow field behind the bluff body. When the BVK instability dominated, the primary frequency of the pressure pulsation aligned with that of the temperature pulsation. Conversely, under the dominance of the KH instability, the temperature pulsation did not exhibit a distinct main frequency. At present, the influence of oxygen content and incoming flow rate on the combustion performance of the combustion chamber is not clear. The study of the effect of oxygen content on the combustion characteristics of the combustion chamber at different incoming flow rates provides a reference for improving the performance of the combustion chamber and enhancing the combustion stability.

Fluid-Dynamic Mechanisms Underlying Wind Turbine Wake Control with Strouhal-Timed Actuation

A reduction in wake effects in large wind farms through wake-aware control has considerable potential to improve farm efficiency. This work examines the success of several emerging, empirically derived control methods that modify wind turbine wakes (i.e., the pulse method, helix method, and related methods) based on Strouhal numbers on the O(0.3). Drawing on previous work in the literature for jet and bluff-body flows, the analyses leverage the normal-mode representation of wake instabilities to characterize the large-scale wake meandering observed in actuated wakes. Idealized large-eddy simulations (LES) using an actuator-line representation of the turbine blades indicate that the n=0 and ±1 modes, which correspond to the pulse and helix forcing strategies, respectively, have faster initial growth rates than higher-order modes, suggesting these lower-order modes are more appropriate for wake control. Exciting these lower-order modes with periodic pitching of the blades produces increased modal growth, higher entrainment into the wake, and faster wake recovery. Modal energy gain and the entrainment rate both increase with streamwise distance from the rotor until the intermediate wake. This suggests that the wake meandering dynamics, which share close ties with the relatively well-characterized meandering dynamics in jet and bluff-body flows, are an essential component of the success of wind turbine wake control methods. A spatial linear stability analysis is also performed on the wake flows and yields insights on the modal evolution. In the context of the normal-mode representation of wake instabilities, these findings represent the first literature examining the characteristics of the wake meandering stemming from intentional Strouhal-timed wake actuation, and they help guide the ongoing work to understand the fluid-dynamic origins of the success of the pulse, helix, and related methods.

Numerical analysis of the flow over four side-by-side square cylinders with different gaps

This study conducts two-dimensional numerical simulations of the flow over four square cylinders arranged side by side at a low Reynolds number (Re) of 100. The investigation primarily centers on the influence of the gap to a square cylinder width ratio (g*) on the flow. The range of g* spans from 0.1 to 7.0. Within this parameter range, three distinct flow regimes emerge based on the inherent flow characteristics. These regimes are defined as follows: (1) single bluff body flow (g* ≤ 0.3), (2) flip-flopping flow (0.3 < g* < 2.0), and (3) modulated periodic flow (g* ≥ 2.0). Additionally, the modulated periodic flow is further categorized into three distinct flow patterns. Various aspects of these different flow regimes are examined, including vortex contours, velocity fields, and liquid force coefficients around the cylinders. Moreover, detailed illustrations are provided for the modulation behaviors in vortex structures and liquid force coefficients. Finally, the proper orthogonal decomposition technique is employed to identify and analyze the underlying spatial coherent structures in the flow field, offering further insights into the dynamic features of wakes.

Shape effect on solid melting in flowing liquid

Iceberg melting is a critical factor for climate change. However, the shape of an iceberg is an often neglected aspect of its melting process. Our study investigates the influence of different ice shapes and ambient flow velocities on melt rates by conducting direct numerical simulations of a simplified system of bluff body flow. Our study focuses on the ellipsoidal shape, with the aspect ratio as the control parameter. We found the shape plays a crucial role in the melting process, resulting in significant variations in the melt rate between different shapes. Without flow, the optimal shape for a minimal melt rate is the disk (two-dimensional) or sphere (three-dimensional), due to the minimal surface area. However, as the ambient flow velocity increases, the optimal shape changes with the aspect ratio. We find that ice with an elliptical shape (when the long axis is aligned with the flow direction) can melt up to 10 % slower than a circular shape when exposed to flowing water. Following the approach considered by Huang et al. (J. Fluid Mech., vol. 765, 2015, R3) for dissolving bodies, we provide a quantitative theoretical explanation for this optimal shape, based on the combined contributions from both surface-area effects and convective-heat-transfer effects. Our findings provide insight into the interplay between phase transitions and ambient flows, contributing to our understanding of the iceberg melting process and highlighting the need to consider the aspect-ratio effect in estimates of iceberg melt rates.

FIV and energy harvesting using bluff body piezoelectric water energy harvester with different cross-sections

Research utilizing piezoelectric fiber composites to power network nodes or micro-sensors by capturing energy from the surrounding environment is becoming a hot spot, and the structural design to efficiently improve the performance of energy harvesting is very important. The performance of a vertical cantilever piezoelectric water energy harvester (PWEH) with three different cross-sections including circular, square and equilateral triangle, each with a mass ratio of 4.8, was investigated at Reynolds number within 770–8800. Emphasis is placed on the effects of the bluff body cross-section, load resistance, and flow velocity on the flow-induced vibration (FIV) and energy response of the vertical cantilever beam of the PWEH. Except for the decreasing amplitude in the lower branch of the circular cylinder water energy harvester (CWEH), there is no distinction in the vibration response branches compared to the classical elastically supported circular cylinder. The resistance has little effect on the vibration response, while it has a significant effect on the voltage and power response. The maximum amplitude and pendulum angle of the square cylinder water energy harvester (SWEH) are slightly larger than those of the CWEH. The maximum voltage and power are smaller for the SWEH than for the CWEH. The equilateral triangular cylinder water energy harvester (TWEH) demonstrates excellent performance. It has a maximum amplitude of 3.8 D, 3.4 times that of the CWEH. The peak pendulum angle of TWCH is 13.9°, 3.2 times that of CWEH. It has a voltage of 0.057 V at a resistance of ∞, which is 3.4 times that of CEWH. In addition, the TWCH has an output power of 0.38 nW at a resistance of 106Ω, which is 9.5 times that of the CWEH. This study suggests that the best energy efficiency of TWEH is achieved by coupling vortex-induced vibration (VIV) and galloping excitation.

Deep reinforcement transfer learning of active control for bluff body flows at high Reynolds number

We demonstrate how to accelerate the computationally taxing process of deep reinforcement learning (DRL) in numerical simulations for active control of bluff body flows at high Reynolds number ( $Re$ ) using transfer learning. We consider the canonical flow past a circular cylinder whose wake is controlled by two small rotating cylinders. We first pre-train the DRL agent using data from inexpensive simulations at low $Re$ , and subsequently we train the agent with small data from the simulation at high $Re$ (up to $Re=1.4\times 10^5$ ). We apply transfer learning (TL) to three different tasks, the results of which show that TL can greatly reduce the training episodes, while the control method selected by TL is more stable compared with training DRL from scratch. We analyse for the first time the wake flow at $Re=1.4\times 10^5$ in detail and discover that the hydrodynamic forces on the two rotating control cylinders are not symmetric.

Flow Structures and Aerodynamic Behavior of a Small-Scale Joined-Wing Aerial Vehicle under Subsonic Conditions

Flow behavior and aerodynamic performance of a small-scale joined-wing unmanned aerial vehicle (UAV) was studied experimentally and numerically under various pitch and yaw angle combinations in subsonic flow conditions. Selected numerical results are compared against experimental results obtained using surface oil flow visualizations and force measurements, with additional simulations expanding the range of combined pitch and yaw configurations. Under zero-yaw conditions, increasing the pitch angle leads to the formation of symmetric ogive vortex roll-ups close to the fuselage and their significant interactions with the fore-wing. Additionally, contributions to lift and drag coefficients under zero-yaw conditions by the key UAV components have been documented in detail. In contrast, when the UAV is subjected to combined pitch and yaw, no clear evidence of such ogive vortex roll-ups can be observed. Instead, asymmetric flow separations occur over the fuselage’s port side and resemble bluff-body flow behavior. Additionally, these flow separations become more complex, and they interact more with the fuselage and fore- and aft-wings when the yaw angle increases. Lift and drag variations due to different pitch and yaw angle combinations are also documented. Finally, rolling and yawing moment results suggest that the present UAV possesses adequate flight stability unless the pitch and yaw angles are high.

Flow structure and dynamics behind cylinder arrays at Reynolds number ∼100

The flow behind nine different arrays of cylinders is experimentally investigated via Particle Image Velocimetry (PIV) at a Reynolds number of Re ∼100 based on the diameter of the cylinders. Each array consists of a column of four cylinders in front and three in the rear. The horizontal distance between the two columns and the vertical distance between the cylinders within each column are varied for H/D=[2,4,8] and V/D=[2,4,6], resulting in nine different arrays denoted as mVnH, where m corresponds to V/D and n stands for H/D. The PIV measurements are conducted for 15 s at 200 Hz frequency, corresponding to 39 to 360 vortex shedding events for the wakes in this study. Then, proper orthogonal decomposition is applied to the velocity fields to analyze the flow dynamics. All arrays show unsteady flow, and based on their flow structures, they are classified in to three main categories of single bluff body (SBB), transitional (TR), and co-shedding (CS) flow. SBB characteristics can be seen for 2V2H and 2V4H arrays, but the latter has more steady vortex shedding as the H/D increases from 2 to 4. Then, 2V8H and 4V2H have an asymmetric flow with several vortex streets and act as an intermediary stage in the shift from SBB to CS flow structure when the distances are increased. The highest total kinetic energy values and widest probability density functions of the velocity components are observed for this group. The five remaining arrays in the CS group have symmetric flow, with three or five vortex streets present behind. However, based on the distances, the frequency and phase synchronization of the vortex streets change considerably, which might have an important effect on, for example, the heat transfer or the structural load of the cylinders.

Self-adaptive turbulence eddy simulation of flow control for drag reduction around a square cylinder with an upstream rod

The use of an upstream circular rod to control the flow around a downstream square cylinder is found to efficiently reduce the drag of the square cylinder. The complex flow characteristics and mechanism of the rod-square system in tandem arrangement as a passive flow control method for various centre-to- centre gap ratios (L/D) are investigated by numerical simulation. Turbulence modelling of the rod-square cylinder system is challenging. To select a suitable turbulence modelling, the recently developed Self-Adaptive Turbulence Eddy Simulations (SATES), as well as IDDES (Improved Delayed Detached Eddy Simulation) and SBES (Stress Blended Eddy Simulation) are first assessed for single circular and single square cylinder flow test cases. The SATES method performs best among the three models for bluff body flow simulation and is thus used in the drag flow control study. For the rod-square flow control system, the Reynolds number is 34000 based on freestream velocity U0 and the edge length of the square cylinder D. The diameter of the control rod is kept constant at d/D = 0.18. The flow characteristics and mechanism are explored in detail, varying the rod and square cylinder distance of L/D = 1.5, 2.0, 2.5and 3.0. According to the absence or presence of vortex shedding from the upstream rod cylinder, two flow patterns (pattern I and pattern II) are observed. Large drag reduction is observed for all the simulation cases the maximum drag reduction is approximately 63% with L/D = 2.0, and the minimum drag reduction approximately 53% with L/D = 3.0. The secondary lock-frequency, which presents as pattern II, is caused by the excitation of upstream vortices. It is found that the side recirculation is associated with the wake recirculation length of the square cylinder, which is similar to the elongated cylinder in the flow pattern I. The flow mechanism of suppression of the vortices from the rod can be attributed to the effective diffusion of vorticity in the separating shear layer caused by the presence of the front wall of the square cylinder.

Numerical simulation of bluff body turbulent flows using hybrid RANS/LES turbulence models

Many engineering applications involve turbulent flows around bluff bodies. Because of their intrinsically unsteady dynamics, bluff body characteristic flows feature unique turbulence-related phenomena, which makes their numerical modeling challenging. Accordingly, accounting for a circular bluff body flow configuration, three different turbulence modeling approaches are investigated in this work, (i) Reynolds-averaged Navier–Stokes (RANS), (ii) large eddy simulation (LES), and (iii) hybrid RANS/LES. Regarding the hybrid approaches, two variants of the detached eddy simulation (DES) one, delayed DES (DDES) and improved delayed DES (IDDES), are studied. As RANS model, the $$\mathrm{k}-\mathrm{\omega SST}$$ is utilized here. This RANS model is also used as the background one for both DDES and IDDES. Wall-adaptive local eddy viscosity (WALE) is used in turn as the sub-grid scale (SGS) model for LES. The velocity two-point correlation function is used to assess the mesh size requirements. When compared to experimental data, the obtained numerical results indicate that RANS overestimates the recirculating bubble length by over 18% and is not capable of describing the turbulent kinetic energy and the flow anisotropy in agreement with the experimental data. In contrast, LES, DDES, and IDDES are all within 1% of the recirculating bubble length while predicting both the Reynolds stress tensor components and the corresponding flow anisotropy in agreement with the measurements. Besides, normalized anisotropy tensor invariants maxima in the shear layer were reproduced by all scale resolving models studied here, but they failed to yield the local extrema measured within the wake recirculation region. A comparative analysis of the anisotropic Reynolds stress tensor invariances underscores the adequacy of the scale resolving models.

Passive Flow Control around Two Side‐by‐Side Square Cylinders Using a Control Plate

This article is concerned with the numerical analysis of reduction of fluid forces (drag and lift) and suppression of vortex shedding around two side‐by‐side square cylinders using the lattice Boltzmann method. For this purpose, a passive flow control methodology is adopted in which a flat plate (termed as the control plate) is placed at the upstream position of cylinders. The gap ratio (g) between the cylinders and the plate is varied from 0 to 4 while the height of the control plate is varied from 0.2 to 0.8 at fixed Reynolds number of 150. Different flow patterns are found in this study depending on the gap ratios and different heights of the control plate. These flow patterns are single bluff body flow, flip‐flopping flow, and antiphase vortex shedding flow patterns. The narrow gap ratio (g = 0.5) is found to have more impact in terms of force reduction and flow control as compared to larger gap ratios. This article also shows that the fluid flow parameters such as the mean drag coefficient, the Strouhal number, and rms values of drag and lift coefficients of both cylinders reduce considerably due to the control plate as compared to without the control plate. In this regard, it is found that the mean drag coefficient of upper cylinder reduces upto 45.94%, the Strouhal number of both cylinders reduces upto 18.66%, while a maximum reduction of 83.47% and 95.39% is observed in root‐mean‐square values of drag and lift coefficients of upper cylinder, respectively. Another important finding of this article is that the control plate does not suppress forces and control flow at all gap ratios and heights of control plate considered in this article. In some cases, the flow‐induced forces were found to be increasing as compared to without the control plate, and this generally happened at higher gap ratios.

Numerical Study on the Flow Past Three Cylinders in Equilateral-Triangular Arrangement at Re = 3 × 106

One of the most common systems in engineering problems is the multi-column system in the form of an equilateral-triangular arrangement. This study used three-dimensional numerical simulations to investigate the flow around three cylinders in this arrangement at the super-critical Reynolds number Re=3×106, concentrating on the influence on the spacing ratio (L/D) among cylinders. The instantaneous vortex structures, Strouhal numbers, fluid force coefficients, and pressure distributions are analyzed thoroughly. The present study demonstrated that fluid dynamics is sensitive to L/D, by which five different flow patterns are classified, namely single bluff body flow (L/D≤1.1), deflected gap flow (1.2≤L/D≤1.4), anti-phase flow (1.5≤L/D≤2.3), in-phase flow (2.5≤L/D<3.5), and co-shedding flow (L/D≥3.5). Critical bounds are identified by significant transitions in the flow structure, discontinuous drop and jump of St, and force coefficients.

Global linear stability analysis of a flame anchored to a cylinder

This study investigates the linear stability of a laminar premixed flame, anchored on a square cylinder and confined inside a channel. Many modern linear analysis concepts have been developed and validated around non-reacting bluff-body wake flows, and the objective of this paper is to explore whether those tools can be applied with the same success to the study of reacting flows in similar configurations. It is found that linear instability analysis of steady reacting flow states accurately predicts critical flow parameters for the onset of limit-cycle oscillations, when compared to direct numerical simulation performed with a simple one-step reaction scheme in the low Mach number limit. Furthermore, the linear analysis predicts a strong stabilising effect of flame ignition, consistent with documented experiments and numerical simulations. Instability in ignited wake flows is, however, found to set in at sufficiently high Reynolds number, and a linear wavemaker analysis characterises this instability as being driven by hydrodynamic mechanisms of a similar nature as in non-reacting wake flows. The frequency of nonlinear limit-cycle flame oscillations in this unstable regime is retrieved accurately by linear eigenmode analysis performed on the time-averaged mean flow, under the condition that the full set of the reacting flow equations is linearised. If, on the contrary, unsteadiness in the density and in the reaction rate are excluded from the linear model, then the congruence between linear and nonlinear dynamics is lost.

Experimental comparative analysis of hybrid energy harvesters exposed to flow-induced vibrations

In this study, hybrid energy harvesting based on electromagnetic induction (EM) and piezoelectric transduction (PZT) is experimentally investigated under different conditions of flow-induced vibrations. The energy harvesting performance of the system is examined when the electromagnetic and piezoelectric mechanisms are used both separately and simultaneously. In this regard, firstly, only electromagnetic induction harvesting structure is attached to a beam, and time-dependent voltage and displacement are experimentally investigated. Then, PZT has adhered to the beam, and voltage outputs are measured in both the PZT and EM circuits. The third scenario is based on removing the electromagnetic harvesting structure and only the piezoelectric energy harvesting performance is studied. The mentioned cases are investigated under different excitation circumstances, that is, distinct bluff-body geometries and flow velocities. While the square bluff-body geometry is connected to the structure, both PZT and EM harvested power are determined by considering different electrical load resistances. It is mainly revealed that the total energy amount is higher in the hybrid configuration. After determining the hybrid structure is the most effective, elements with different splitters geometry are attached to the bluff-body geometry of the harvesting structure. Finally, the vibration enhancement potential of these new types of splitters on the harvesting structure is experimentally investigated. For the solo electromagnetic harvester, the maximum power is obtained at an external load resistance value of 10 kΩ, while for the solo PZT harvester, the maximum power is observed at the resistance value of 330 kΩ. Among the three types of splitter geometries examined, the highest voltage was obtained from type-1 as 14.168 V.

Identification and reconstruction of high-frequency fluctuations evolving on a low-frequency periodic limit cycle: application to turbulent cylinder flow

Oftentimes, turbulent flows exhibit a high-frequency turbulent component developing on a strong low-frequency periodic motion. In such cases, the low-frequency motion may strongly influence the spatio-temporal features of the high-frequency component. A typical example of such behaviour is the flow around bluff bodies, for which the high-frequency turbulent component, characterized by Kelvin–Helmholtz structures associated with thin shear layers, depends on the phase of the low-frequency vortex-shedding motion. In this paper, we propose extended versions of spectral proper orthogonal decomposition (SPOD) and of resolvent analysis that respectively extract and reconstruct the high-frequency turbulent fluctuation field as a function of the phase of the low-frequency periodic motion. These approaches are based on a quasi-steady (QS) assumption, which may be justified by the supposedly large separation between the frequencies of the periodic and turbulent components. After discussing their relationship to more classical Floquet-like analyses, the new tools are illustrated on a simple periodically varying linear Ginzburg–Landau model, mimicking the overall characteristics of a turbulent bluff-body flow. In this simple model, we in particular assess the validity of the QS approximation. Then, we consider the case of turbulent flow around a squared-section cylinder at a Reynolds number of $Re=22\,000$ , for which we show reasonable agreement between the extracted spatio-temporal fluctuation field and the prediction of QS resolvent analysis at the various phases of the periodic vortex-shedding motion.

An investigation of bluff body flow structures in variable velocity flows

The present study explores three-dimensional vortex-dynamics past a wall-attached bluff body kept in a variable velocity field with numerical simulations. A trapezoidal pulse of mean velocity, consisting of acceleration phase from rest followed by constant velocity phase and deceleration phase to rest, is imposed at the inlet of the computational domain similar to the experimental study of Das et al. [“Unsteady separation and vortex shedding from a laminar separation bubble over a bluff body,” J. Fluids Struct. 40, 233–245 (2013)]. For a wide range of Reynolds numbers (96≤Reb≤2390), acceleration Reynolds numbers (196≤Rea≤978), and deceleration Reynolds numbers (310≤Red≤1522), different stages of flow evolution are systematically analyzed. The flow evolution starts with the formation of a primary vortex followed by a two-dimensional circular array of spanwise vortex tubes by inflectional shear-layer instability. At a sufficiently high Reynolds number, the shear layer vortices originated from two-dimensional fluctuations deformed by three-dimensional instabilities, giving fragmented streamwise vorticity. In addition, long-wavelength “tongue-like structures” and short-wavelength “rib-like structures” are evident near the top wall and the bluff body, respectively. The streamwise vorticity generation equation indicates that the spanwise vortex tubes initially tilt, resulting in streamwise vorticity, further amplified by the vortex stretching process. The distinct flow features, including mode shape, frequency, and growth rate associated with the shear-layer instability, are identified using the dynamic mode decomposition (DMD) algorithm. Using the maximum growth rate criteria, the DMD technique successfully separates the coherent shear layer modes associated with two-dimensional shear layer instability from the flow field.