Two-dimensional Circular Cylinder Research Articles

A data–driven sensibility tool for flow control based on resolvent analysis

This study presents a novel application of data-driven resolvent analysis algorithm for flow control. The objective is to identify key coherent structures connected to regions of the flow that are highly sensitive to structural changes. Modifying such regions, i.e., including momentum source terms, flow stabilizers, or changing the shape of the body under study, we can control the appearance of flow instabilities. The method is tested in two different applications: the laminar flow behind a two-dimensional circular cylinder and a turbulent channel flow including heat transfer to the endwall. In the first test case, the flow unsteadiness is controlled by including two stabilizers (formed by two small cylinders) in the areas suggested by resolvent analysis. This is a benchmark problem in fluid dynamics that serves to validate the idea of using this tool for flow control. In the second test case, data-driven resolvent analysis is applied as a mean to control, enhance or reduce, convective heat transfer. Modifications in the geometry, in the form of cavities and ribs included in the areas pointed by resolvent analysis, show the possibility of enhancing heat transfer while reducing drag. The findings highlight the importance of resolvent analysis in understanding flow dynamics and designing effective flow control strategies.

Computational aeroacoustics and phase-conjugation technique for localizing flow-induced sources

This paper presents a framework comprising computational aeroacoustics (CAA) solvers and a numerical phase-conjugation technique to localize flow-induced noise sources generated by bodies immersed in low Mach number flows. Two test-cases were considered, namely, flow over a two-dimensional (a) circular cylinder at Reynolds number Re =150 and Mach number M = 0.2 and (b) NACA-0012 airfoil at Re = 5000 and angle of attack (AoA) α = 5 deg. The CAA simulations were carried out in OpenFOAM wherein the two-dimensional unsteady, incompressible Navier–Stokes equations was solved using either the pressure-implicit splitting of operators (PISO) algorithm or large eddy simulation (LES). The near-field aerodynamic sources were extracted in terms of the unsteady Lighthill stress tensor terms, following which the far-field acoustic data were computed on boundary nodes using different methods which include the numerical solution of the Lighthill equation, Curle’s analogy, and Ffowcs Williams and Hawkings (FWH) analogy as well as linearized Euler equations (LEE). Next, the frequency-domain phase-conjugation (PC) method was implemented in the finite-element (FE) based COMSOL software to reconstruct the radiated acoustic pressure field, whereby the dipole source location was readily identified by pair of focal spots at the cylinder or at the airfoil trailing-edge (TE).

Cylinder water entry on a perturbed water surface

The perturbations existing on a breaking wavefront can be a potential explanation for the slamming pressure variability in wave impacts. Here, we investigate the effect of these perturbations by forced vertical slamming of a two-dimensional circular cylinder with constant downward velocity on standing waves. Through experimental modelling and numerical simulation, the slamming force is measured for several standing wave amplitudes and wavelengths. The standing wave phase is tuned such that the impact occurs symmetrically at the instant of maximum crest or trough. Our observations show that slamming coefficients vary with the standing wave amplitude when the wavelength is kept constant and vice versa. The trough impact slamming coefficient can be more than two times the flat impact, and up to four times the crest impact. The experimental results are reproduced by numerical simulations and they agree reasonably well in general. Two analytical approaches based on the von Kármán (NACA, vol. 321, 1929, pp. 1–8) and Wagner (Z. Angew. Math. Mech., vol. 12, 1932, pp. 913–215) methods, which consider the effect of water surface curvature, are introduced. The slamming coefficient calculated from these methods can provide a bound in which the slamming coefficient can be found for each standing wave amplitude and wavelength. Further insight is achieved by numerical simulations of impact on the shorter wavelength to diameter ratio of$0.05<\lambda /D<0.4$. As the wavelength to diameter ratio becomes smaller, the cylinder impacts the water surface at several locations. As a result, multiple peaks occur, and the trapped air at different locations between the cylinder and the water surface yields oscillations with different frequencies on the slamming coefficient time history.

Effect of Cross Thermal Buoyancy on Cu–H2O Nanofluid Flow Over Bluff Objects at Low Reynolds Numbers

Increasing the solid volume fraction (φ) in a nanofluid may trigger the vortex shedding around a bluff object even for a low Reynolds number (Re) steady regime. The cross thermal buoyancy may also trigger the vortex shedding around bluff objects at low Re. When the nanofluid flow is subjected to cross buoyancy, the initiation of the vortex shedding process around bluff objects could be accelerated. For a given range of Re, thermal buoyancy and solid volume fraction decide the characteristics of the flow. Both these two parameters can separately have a critical value at which the shedding process initiates. However, the presence of one parameter could affect the other significantly. In order to substantiate the above facts, a two-dimensional numerical simulation is performed to study the effect of cross thermal buoyancy on the free stream nanofluid (Cu–H2O) flow over two-dimensional square and circular cylinders. The initiation of the shedding process is observed for 10 ≤ Re ≤ 30 and 0% ≤ φ ≤ 10% through computation of the critical Richardson numbers for all the φ in the range. The relevant flow and thermal parameters are also computed to further establish the facts.

Lifting Stokes' paradox by accelerating flow past a circular cylinder and extension of the analysis to the sphere

It is known that Stokes' paradox exhibits in various flow conditions, most notably, in flow past a two-dimensional (2D) circular cylinder. In this study, we provide an example through detailed analytical solution that Stokes' paradox can be lifted by accelerating flow past a stationary cylinder. The analysis is also extended to the case of the accelerating flow past a stationary sphere although in this case, there is no Stokes' paradox. The effects of the acceleration parameter on the flow streamlines, the pressure, and the vorticity distributions, as well as on the drag coefficient, are investigated. The drag comprises the potential component and vorticity component, which are further due to form drag and frictional drag receiving a separate investigation. However, the drag decomposition is also examined the viewpoint of the force decomposition: the total drag = the potential component + surface vorticity component + volume vorticity component.

Exploring hidden flow structures from sparse data through deep-learning-strengthened proper orthogonal decomposition

Proper orthogonal decomposition (POD) enables complex flow fields to be decomposed into linear modes according to their energy, allowing the key features of the flow to be extracted. However, traditional POD requires high-quality inputs, namely, high-resolution spatiotemporal data. To alleviate the dependence of traditional POD on the quality and quantity of data, this paper presents a POD method that is strengthened by a physics-informed neural network (PINN) with an overlapping domain decomposition strategy. The loss function and convergence of modes are considered simultaneously to determine the convergence of the PINN-POD model. The proposed framework is applied to the flow past a two-dimensional circular cylinder at Reynolds numbers ranging from 100 to 10 000 and achieves accurate and robust extraction of flow structures from spatially sparse observation data. The spatial structures and dominant frequency can also be extracted under high-level noise. These results demonstrate that the proposed PINN-POD method is a reliable tool for extracting the key features from sparse observation data of flow fields, potentially shedding light on the data-driven discovery of hidden fluid dynamics.

Validation of SST-SCM correlation-based transition model by the simulation of wall-bounded flows

A modified correlation-based transition model coupled with SST turbulence model(k−ω−γ−R˜eθt) is proposed in this work. For better verification of intermittency, the constraint definition strictly based on local variables is cited to ensure physical solution. In order to obtain more details of laminar and transition boundary layer for separation-induced transition, a local correction method based on streamline curvature modification (SCM) has been developed to extend model ability in predicting adverse-pressure-gradient flows. The mean strain rate involved with mean rotation rate and shear rate is modified according to wall-bounded condition with rotation and non-rotation features to preserve the anisotropic characteristics encountered in large range flows. Furthermore, separation-induced intermittency is corrected by considering the effect of average strain rate to prevent outliers in local intermittency whenever the laminar boundary layer separates. Considering that results of test cases simulation with different empirical correlations vary huge from each other, all cases are matched with its suitable empirical correlations to ensure the stability and accuracy calculated by proposed model. Transitional flat-plate cases are calculated to validate the basic ability for near-wall flow simulation.Massive separated flow over two-dimensional circular cylinder has been studied to verify the predicted accuracy for non-equilibrium flows. Flow over multi-element airfoil 30P30N and the simulation of vortex system over three-dimensional Low Pressure Turbine(LPT) cascade T106A are given to examine the predictions of Reynolds shear stress profiles and pressure distribution with flow disturbance; reasonable results show a good match between experimental data and calculation by proposed model.

Effect of synthetic jet on circular cylinder radiated noise in laminar flow state

This article focuses on the effect of active control via synthetic jets (SJs) on sound generated by a two-dimensional circular cylinder by using the acoustic analogy method. The cylinder is immersed in a uniform upstream flow, where the corresponding Reynolds number is 100 and the Mach number is 0.1. A pair of SJs is placed near the cylinder’s separation point issuing periodically varying forcing, with different combinations of forcing frequency and phase difference. The lattice Boltzmann method (LBM) is coupled with the multi-direct forcing immersed boundary method to solve the near-field flow dynamics. The mechanism of the sound generation lies in the fact that pressure pluses are induced by the periodic vortex shedding from the cylinder’s surface, i.e. dipoles. In the case with active flow control, extra monopoles are generated by the unsteady flow rate resulting from the SJs' periodic blow/suction. The interaction between monopoles and dipoles is confirmed to have a big influence on the acoustic field. The acoustic analogy method is used in various cases with a wide range of control parameters, because it has a considerably lower computational cost than the direct simulation method. Taking into account the effect of the monopole, the acoustic analogy method is developed for solving two-dimensional sound field by substituting the Green’s function. Results indicate that the primary lock-on and the secondary lock-on occur in the case of specified control parameters. The frequency of vortex shedding is related to the SJs’ frequency, deviating from the unforced frequency. Owing to the noise induced by flow, the frequency and phase difference of the SJs also have significant influence on sound field. The far-field noise is enlarged although the SJs reduce drag, due to the induced extra monopole, as well as the strengthened hydrodynamic fluctuation. Further increasing SJs’ frequency or reducing the phase difference will enlarge the far-field noise and make the directivity transformed from dipole to monopole, since the SJs’ self-noise is stronger. Moreover, it is found that the acoustic power increases approximately 4–18 dB compared with the unforced circular cylinder and the drag dipole is strengthened in all combinations of control parameters. This study deepens the understanding of the effect of SJs on sound field, and provides a reference for future studying the control strategies of suppressing noise generated from bluff bodies.

A hybrid reduced-order model combing deep learning for unsteady flow

Reduced-order models such as dynamic mode decomposition (DMD) and proper orthogonal decomposition (POD) have been extensively utilized to model unsteady flow. Although the major flow patterns can be captured by DMD and POD, due to the linear assumption, the modeling accuracy is low for complex and strongly nonlinear flow structures such as shock wave and vortex. To improve the accuracy and robustness of predicting unsteady flow, this work proposes a novel modeling method based on a hybrid reduced-order model. Since the flow can be regarded as a fusion of the main flow and the residual flow from a modeling perspective, the hybrid reduced-order model is constructed by DMD and POD, which are, respectively, used to obtain different flow properties. First, DMD is applied in describing the main flow, which contains the dominant modes determining most properties of the flow. Then, POD combining the long short-term memory is conceived to model the residual flow that the DMD cannot capture, to further enhance the modeling accuracy. The proposed method is validated by modeling two unsteady flows, which are the flow past a two-dimensional circular cylinder at Reynolds number 100 and the forced oscillation of an airfoil at transonic speed. The results indicate that the proposed method with proper modeling efficiency gains better accuracy and robustness than the existing methods. In particular, this approach has better forecasting accuracy of shock wave and vortex.

Active flow control using deep reinforcement learning with time delays in Markov decision process and autoregressive policy

Classical active flow control (AFC) methods based on solving the Navier–Stokes equations are laborious and computationally intensive even with the use of reduced-order models. Data-driven methods offer a promising alternative for AFC, and they have been applied successfully to reduce the drag of two-dimensional bluff bodies, such as a circular cylinder, using deep reinforcement-learning (DRL) paradigms. However, due to the onset of weak turbulence in the wake, the standard DRL method tends to result in large fluctuations in the unsteady forces acting on the cylinder as the Reynolds number increases. In this study, a Markov decision process (MDP) with time delays is introduced to model and quantify the action delays in the environment in a DRL process due to the time difference between control actuation and flow response along with the use of a first-order autoregressive policy (ARP). This hybrid DRL method is applied to control the vortex-shedding process from a two-dimensional circular cylinder using four synthetic jet actuators at a freestream Reynolds number of 400. This method has yielded a stable and coherent control, which results in a steadier and more elongated vortex formation zone behind the cylinder, hence, a much weaker vortex-shedding process and less fluctuating lift and drag forces. Compared to the standard DRL method, this method utilizes the historical samples without additional sampling in training, and it is capable of reducing the magnitude of drag and lift fluctuations by approximately 90% while achieving a similar level of drag reduction in the deterministic control at the same actuation frequency. This study demonstrates the necessity of including a physics-informed delay and regressive nature in the MDP and the benefits of introducing ARPs to achieve a robust and temporal-coherent control of unsteady forces in active flow control.

Irregular vortex-induced vibrations of a two-dimensional circular cylinder at a low Reynolds number

Irregular vortex-induced vibrations (VIV) of a two-dimensional circular cylinder, characterized by the time-varying oscillation amplitude and frequency, were observed in both experiments and numerical simulations. This paper attempts to elucidate the phenomena by numerical simulations of a circular cylinder in VIV, with mass ratios of 2, 10 and 50, at a Reynolds number of 150. The lift force acting on the cylinder is assumed to be a sum of two components associated with added mass and hydrodynamic damping. The time-dependent added-mass and hydrodynamic damping coefficients are determined by the least-squares fit of lift from the cylinder displacement. The effective natural frequency varies with time due to the added mass, and the cylinder oscillation amplitudes are influenced by the hydrodynamic damping force. Consequently, VIV irregularities arise from the complex evolution of the added-mass and hydrodynamic damping coefficients. The irregular oscillations are associated with the interaction of vortices in the near wake, which results in the intermittent appearance of disorganized Karman vortex street. Moreover, the vortex interactions involve a rapid reduction of the hydrodynamic damping coefficients. Besides, the irregular oscillation region is identified in terms of the reduced velocity, and smaller mass ratio tends to have larger width of the region.

Numerical investigations of the wake behind a confined flat plate

The two-dimensional flow around a confined flat plate is simulated with the spectral element code, Nek5000. Direct numerical simulations were carried out at low Reynolds numbers Re (between 10⩽Re⩽200) and various blockage ratios β (between 0.1⩽β⩽0.9) and compared with the confined two-dimensional circular cylinder flow previously reported by Sahin and Owens (2004). Four distinct flow regimes are observed for the flow over a confined flat plate. The first is a steady symmetric wake where the vortices are evenly distributed along the centerline of the channel. The second is an unsteady symmetric regime which upon time-averaging the instantaneous flow field, the wake profile is symmetric. The third is an asymmetric steady wake where the flow is steady but the vortices in the wake are skewed towards one of the channel walls. The first three have been reported for the confined flow over a circular cylinder. However, a fourth flow regime defined as unsteady asymmetric wake is found for a flat plate at β = 0.8. This flow regime was not reported in prior studies on the confined flow over a confined cylinder. Analysis using linear stability analysis is also reported in this paper which confirms the trends reported in this paper. Effects of the confinement on the wake of a flat plate on the hydrodynamic forces such as the mean drag coefficient and Strouhal number have also been documented for the same range of Re and β and compared with the flow over a confined cylinder.

平面衝撃波が様々な姿勢の円柱に及ぼす非定常流体力の研究

Studying the reflection and diffraction of shock waves generated around complex shapes is essential to clarify the blast phenomena caused by objects. In this study, a two-dimensional circular cylinder and a flow field impinging on a three-dimensional circular cylinder were analyzed by CFD using the three-dimensional Euler equations and the immersed boundary method. As a result, we confirmed pressure distributions that qualitatively simulated the previous study and the experimental results. However, more detailed discussions on the reflection and diffraction of shock waves are needed.

Flow characteristics of elastically mounted slit cylinder at sub-critical Reynolds number

The present work numerically investigates vortex-induced vibrations (VIV) of a two-dimensional circular cylinder with an axisymmetric slit at Reynolds number 500. The study examines the effects of slit shape (i.e., converging, diverging, and parallel slits), the effect of slit-area ratios, slit width, and its angle with the freestream velocity on aerodynamic forces, vibration response, and associated flow characteristics. The results demonstrate that the addition of the slit assists the VIV suppression by adding an extra amount of flow to the main flow. It results in the stabilized wake with the pressure recovery downstream of the cylinder and causes a reduction in the lift force over the cylinder. Also, there exist different shedding patterns associated with different slit shapes. A proper orthogonal decomposition of the flow field suggests that among all the three slits, the parallel slit heavily modifies the flow behind the cylinder by distributing the amount of energy to a large number of modes as compared to other slits (converging slit and diverging slit), where the most of the energy is contained in a couple of modes. Further, increasing the slit angle (for parallel slit) with respect to the freestream increases the slit effectiveness up to a specific value of slit-angle and beyond that starts to affect the VIV suppression adversely. Observations for the effect of slit width are also reported from the perspective of suppression of VIV.

Numerical simulations of flow through a variable permeability circular cylinder

This paper investigates flow through variable permeability, two-dimensional circular cylinders using a pseudospectral numerical model. Two types of permeability (K) distributions are considered: constant with a lower permeability blockage, and constant with a higher permeability duct. Boundary conditions set by external flow with high Reynolds number lead to streamwise flow asymmetry and more short length scale variability within the cylinder when compared to conditions set by potential flow. High permeability belts are observed to guide flow around regions of lower permeability, while low permeability belts are observed to impede flow from reaching areas surrounded by the low permeability region. Inward surface flux is used to quantify changes in flow through variable permeability cylinders relative to the constant permeability cylinder. For blocking cases, the relationship between ΔK/K0 and the largest possible change in relative surface flux is nearly linear. In ducting simulations, where ΔK/K0∼1 to ∼10, this relationship is no longer linear. Simple polynomial fits are derived for both situations, allowing for the calculation of the change in permeability required to achieve a given increase or reduction in inward flux. Finally, the numerical results are contrasted with theoretical perturbation results for the case of azimuthal variations in permeability, which lead to a fundamentally different pressure distribution.

Clusters and coherent voids in particle-laden wake flow

Inertial point particles suspended in a two-dimensional unsteady circular cylinder flow at Re=100 are studied by one-way coupled three-dimensional numerical simulations. The striking clustering pattern in the near-wake is strongly correlated with the periodically shed Kármán vortex cells. The particles are expelled from the vortex cores due to the centrifugal mechanism and coherent voids encompassing the local Kármán cells are therefore observed. The particle clustering at the upstream side of each void hole form a smooth edge, where the particle velocity magnitude is consistently lower than at the downstream edge of the voids. The trajectories of these particles originate from the side of the cylinder where the sign of vorticity is opposite to that of the vortex encompassed by the corresponding void hole. The particles are seen to decelerate along a substantial part of their trajectories. Particle inertia is parameterized by means of a Stokes number Sk and smooth edges around the void holes still exist when Sk is increased, although their formation is delayed due to larger inertia. Increasing inertia contributes to a decoupling of the particle acceleration from the slip velocity, which almost coincided at Sk=1.

Experimental investigation of the effects of length-to-diameter ratio of hot-wire sensor on the dynamic response to velocity fluctuations

This paper reconsidered the criterion on the length-to-diameter ratio (l/d) of the hot-wire sensor, $$l/d \ge 200$$ , for end-conduction effects on the dynamic response of constant-temperature hot-wire anemometer (CTA) to be neglected. Experiments were first conducted using a low-noise compact CTA with hot-wire sensors of l/d = 80, 120, 150 and 200 in a two-dimensional (2-D) circular cylinder wake at a Reynolds number Re = 77, at which a 2-D von Karman vortex street developed, allowing us to exclude spatial filtering and tangential velocity effects. The damping coefficient in the CTA bridge was tuned to 0.70 for all sensors to reduce possible influences of over- or under-damping on measurements in a frequency range up to 6 kHz. The stubs and prongs of probes consisted of identical materials and dimensions so that the thermal properties were considered to be identical for all probes. Careful comparisons of the amplitudes of the fundamental (1.9 kHz) and higher harmonic components of time-periodic wake vortices showed that the attenuation due to the end-conduction effect in the absence of the spatial filtering and damping coefficient effects was at most 2.5% in terms of the rms value of velocity fluctuations even for l/d = 80. The similar weak attenuation (about 2.6% for l/d = 80) was also observed in the measurements of low-frequency free-stream turbulence. In addition, effects of l/d on the yaw angle response of the sensor were examined in the free stream, revealing that the yaw angle ( $$\psi $$ ) variation of the measured velocity (both the mean and fluctuations) obeyed the cosine law for $$\psi \le 60^\circ $$ . The Champagne constant k was 0.12 for l/d = 200 and 0.2 even for l/d = 80 in the mean velocity measurement using the present probe with long stubs. On the other hand, the intensity of free stream turbulence measured using a $$45^\circ $$ -yawed sensor was significantly affected by the sensor’s l/d; the rms value of velocity fluctuation was attenuated by about 7.5% for l/d = 80.

Numerical Computation of Low Reynolds Number Viscous Flow Past Bluff Bodies

This article presents a two-dimensional steady viscous flow simulation past circular and square cylinders at low Reynolds numbers (based on the diameter) by the finite volume method with a non-orthogonal body-fitted grid. Diffusive fluxes are discretized using central differencing scheme, and for convective fluxes upwind and central differencing schemes are blended using a ‘deferred correction’ approach. A simplified pressure correction equation is derived, and proper under-relaxation factors are used so that computational cost is reduced without adversely affecting the convergence rate. The governing equations are expressed in Cartesian velocity components and solution is carried out using the SIMPLE algorithm for collocated arrangement of variables. The mesh yielding grid-independent solution is then utilized to study, for the very first time, the effect of the Reynolds number on the separation bubble length, separation angle, and drag coefficients for both circular and square cylinders. Finally, functional relationships between the computed quantities and Reynolds number (Re) are proposed up to Re = <i>40</i>. It is found that circular cylinder separation commences between Re= <i>6.5-6.6</i>, and the bubble length, separation angle, total drag vary as Re, Re<i>−0.5</i>, Re<i>−0.5</i> respectively. Extrapolated results obtained from the empirical relations for the circular cylinder show an excellent agreement with established data from the literature. For a square cylinder, the bubble length and total drag are found to vary as Re and Re<i>−0.666</i>, and are greater than these for a circular cylinder at a given Reynolds number. The numerical results substantiate that a square shaped cylinder is more bluff than a circular one.

Dynamic analysis of a multilayered piezoelectric two-dimensional quasicrystal cylindrical shell filled with compressible fluid using the state-space approach

The state-space approach is developed to analyze the dynamic behaviors of a multilayered two-dimensional piezoelectric quasicrystal circular cylinder filled with the compressible fluid. With simple support at both ends, the hollow cylindrical shell has imperfect bonding between the layers. The analytical solution of a homogeneous cylindrical shell has been derived based on the state equations. The general solution for the corresponding multilayered case is also obtained by utilizing the propagator matrix method. The numerical results present the natural frequencies in free vibration with different length-to-radius and radius-to-thickness ratios. The critical load and dynamic behaviors of the model are exactly predicted in the axial buckling problem. For the impulse case, the influences of the density of the filled fluid and coefficients of interfacial imperfections on the dynamic responses are also discussed.

Predicting wind pressures around circular cylinders using machine learning techniques

Numerous studies have been carried out to measure wind pressures around circular cylinders since the early 20th century due to its engineering significance. Consequently, a large amount of wind pressure data sets have accumulated, which presents an excellent opportunity for using machine learning (ML) techniques to train models to predict wind pressures around circular cylinders. Wind pressures around smooth circular cylinders are a function of mainly Reynolds number (Re), turbulence intensity (Ti) of the incident wind, and circumferential angle of the cylinder. Considering these three parameters as the inputs, this study trained two ML models to predict mean and fluctuating pressures respectively. Three machine learning algorithms including decision tree regressor, random forest, and gradient boosting regression trees (GBRT) were tested. The GBRT models exhibited the best performance for predicting both mean and fluctuating pressures, and they are capable of making accurate predictions for Re ranging from 104 to 106 and Ti ranging from 0% to 15%. It is believed that the GBRT models provide an efficient and economical alternative to traditional wind tunnel tests and computational fluid dynamic simulations for determining wind pressures around two-dimensional smooth circular cylinders within the studied Re and Ti range.