Time-averaged Lift Coefficients Research Articles

Numerical Study of Transonic Buffet on SC(2)-0518 and OAT15A with Vortex Generators

Predicting the transonic buffet and its onset is important for ascertaining the performance limits of an aircraft at its critical angle of attack. Additionally, a physical understanding of the buffet suppression technique is important for preventing shock wave oscillations. In this study, we conducted zonal detached-eddy simulations to numerically investigate the effects of vortex generators (VGs) on buffet suppression and to discuss the differing flow characteristics of the SC(2)-0518 and OAT15A supercritical airfoils when the chordwise position of the VGs is varied. The results for both airfoils equipped with VGs demonstrated significant suppression of large-scale lift oscillations across all calculation steps. VGs placed at 10% of the chord (10%c) from the leading edge produced higher time-averaged lift coefficients for both airfoils, with the OAT15A airfoil showing a particularly notable 2.5% improvement in lift coefficient, leading to a 0.82% increase in L/D ratio. The visualized results indicated that the interaction between the shock wave and VGs leads to variations in the separation point, depending on the VG chordwise position. This separation is affected by the aerodynamic characteristics of the airfoil shapes and the wake induced by the VGs, ultimately resulting in changes to the lift coefficient.

Near-Field Aeroacoustic Shape Optimization at Low Reynolds Numbers

We investigate the feasibility of gradient-free aeroacoustic shape optimization using the flux reconstruction (FR) approach to study two-dimensional flow at low Reynolds numbers. The overall sound pressure level (OASPL) is computed via the direct acoustic approach, and optimization is performed using the gradient-free mesh adaptive direct search (MADS) algorithm. The proposed framework is assessed across three problems. First, flow over an open cavity is investigated at a Reynolds number of Re=1500 and freestream Mach number of M∞=0.15, resulting in a 7.9 dB noise reduction. The second case considers tandem cylinders at Re=200 and M∞=0.2, achieving a 16.5 dB noise reduction by optimizing the distance between the cylinders and their diameter ratio. Finally, a NACA0012 airfoil is optimized at Re=10,000 and M∞=0.2 to reduce trailing edge noise. The airfoil’s shape is optimized to generate a new four-digit NACA airfoil at an appropriate angle of attack to reduce OASPL while maintaining the baseline time-averaged lift coefficient and preventing an increase in the baseline time-averaged drag coefficient. The optimized airfoil is silent at 0 dB and the drag coefficient is decreased by 24.95%. These results demonstrate the feasibility of shape optimization using MADS and FR for aeroacoustic design.

Flow past rotating cylinders using deterministic vortex method

This study examines the performance of an in-house code based on a deterministic vortex method on circular and square cylinders rotating with constant velocity. Subjecting a bluff body to rotary about its axis effectively reduces drag forces, suppresses the fluctuating forces, and increases the lift forces (known as the Magnus effect). Rotating cylinders are well known for their use in rotor ships, rotor aircrafts, and wind turbines. This study aims to establish the accuracy of the in-house code for the rotating circle cylinders based on the results from the literature and examine the behavior of the rotating square cylinders (a less-studied case). A square section, as a many-sided shape, can be considered when the behavior of more complex geometries is of interest, such as trajectories of the sediments, or replacing circular sections when autorotation is of importance. Both cylinders are exposed to a uniform flow of Re = 200 and an imposed rotation rate range of 0 ≤ α ≤ 5.5 for the circular, and 0 ≤ α ≤ 5 for the square cylinder. The present numerical tool is able to predict the vortex shedding suppression as a result of forced rotation. For both cases, a systematic increase in the time-averaged lift coefficient (≈25.5 for the circular and ≈26 for the square case when α = 5) and a general descending trend in the time-averaged drag coefficient (≈0.03 for the circular and ≈0 for the square case when α = 5) are detected. The second mode of vortex shedding for the circular cylinder is captured within a narrow range of rotation rates. A noticeable feature of the flow over rotating square cylinders is the emergence of near-field wakes in the near-body region, which develop independently from the wake behind the body. To the best of the authors’ knowledge, this is the first comprehensive study of a rotating body carried out using a deterministic vortex method-based numerical tool.

The time-averaged aerodynamic performance of three circular columns arranged inline at a subcritical Reynolds number

This study conducted a series of wind tunnel tests to present the time-averaged aerodynamic performance of three equidistant circular columns arranged inline at various incidence angles and center-to-center pitch ratios under a subcritical Reynolds number of 6.4 × 104. The incidence angle α and pitch ratio L/D change in the range of 0°–90° and 1.2–4.0, respectively. The results show that the time-averaged aerodynamic performance of the three columns varies significantly with α as well as L/D. Based on the pitch ratio, the time-averaged aerodynamic coefficients can be approximately classified into four types: minimum pitch ratios (1.2≤L/D < 1.4), small pitch ratios (1.4≤L/D < 2.5), medium pitch ratios (2.5≤L/D < 3.5), and large pitch ratios (3.5≤L/D ≤ 4.0). The aerodynamic interference of the time-averaged aerodynamic coefficients under these four types is discussed by comparing the results obtained for the three columns with those for a single one. The time-averaged drag coefficient mainly experiences a reducing effect at the minimum and small pitch ratios and a certain extent of amplifying effect at the medium pitch ratios. The time-averaged lift coefficient appears non-zero values at some incidence angles, the range of which depends on the pitch ratio. The mechanism of the aerodynamic interference is also discussed by analyzing the time-averaged wind pressure distribution.

Post-stall flow control on aerofoils by leading-edge flags

Self-excited oscillations of flags attached at the leading edge of aerofoils have been investigated at post-stall angles of attack at a chord Reynolds number of 100 000. Significant increases in the time-averaged lift coefficient and stall angle have been observed for three aerofoils: one symmetric, one cambered and one with a sharp leading edge. The aerodynamic improvement is due to the periodic formation of vortices caused by the flag oscillations. When the flag is near the aerofoil surface, it is lifted upwards by the induced velocity of the growing vortex. As the flag moves up, the vortex grows in strength and reaches maximum circulation when the flag is furthest from the aerofoil surface and subsequently sheds. Flags with large stiffness exhibit better spatial and temporal coherence of flag oscillations than the compliant flags, resulting in a larger maximum lift coefficient and higher stall angle. For all aerofoils tested, the best lift enhancement with respect to the clean aerofoils is found when the angle of attack is 6° to 10° above the stall angle of the clean aerofoil. High lift is observed when the flags are locked in with the wake instability in a narrow frequency band, depending on the flag mass ratio and length.

Effect of wing planform on plunging wing aerodynamics

The unsteady aerodynamics of three plunging wings with different planform shapes was investigated in water tunnel experiments by means of force/moment and three-dimensional volumetric velocity measurements at a post-stall angle of attack. In contrast with a rectangular wing, a tapered wing does not exhibit a local minimum of the time-averaged lift coefficient at a reduced frequency of k≈ 1.7. This is due to the oblique shedding of trailing-edge vortices, which prevents the coupling with leading-edge vortices. The wing with a round-tip exhibits the same double maxima that correspond to the subharmonic and the fundamental frequency of vortex shedding in steady freestream. However, combined leading-edge and tip vortex produce larger time-averaged lift force with increasing reduced frequency. The variation of the bending moment is similar to that of the lift force in general. However, the mean bending moment arm shifts outboard with increasing reduced frequency due to the increased three-dimensionality of the vortex filaments and the tip-vortex effect. Maximum lift and bending moment become more similar for all three wings at higher reduced frequencies as the added mass effect becomes more significant.

Numerical Investigation of Vortex Shedding from a 5:1 Rectangular Cylinder at Different Angles of Attack

Although flow around a 5:1 rectangular cylinder at small angles of attack (AoA) has been extensively studied, when the AoA becomes larger, the research is rare. Therefore, this study performs Unsteady Reynolds-Averaged Navier-Stokes simulations (URANS) using the k-ω SST turbulence model for unsteady flow around a two-dimensional 5:1 rectangular cylinder at different AoAs up to 45°. A strong dependence of the flow characteristics on AoA is observed through the analysis of the time-averaged lift coefficient, drag coefficient, and Strouhal number. The peak of lift and drag coefficient is observed to be correlated, respectively, to the leading- and trailing-edge vortex based on the analysis of the flow. The x′-directional length of the main recirculation bubble on the top side and the distance from the bubble center to the leading edge of the cylinder both reach the maximum when α = 15°. In addition, the standard deviation σx′ of the time-averaged velocity U¯x′ along the cylinder shows a trend of increasing at first and then decreasing, and that σy′ also shows the same trend at α = 20°~45°; it fluctuates within a range of 0.05~0.2 at α = 0°~20°. Finally, two principal modes of vortex shedding are observed with α = 15° being their turning point, (i) “1 + 1” mode: in one vortex shedding period, two major vortices shed off from the top and bottom sides of the cylinder at α ≤ 15°; (ii) “2 + 2” mode, four vortices shed off from the top and bottom sides of the cylinder at α &gt; 15° in one vortex shedding period.

Numerical investigation of flow around two cylinders in tandem above a scoured bed

Flow mechanisms around two cylinders in tandem arrangement above a scoured bed have been investigated using the three-dimensional unsteady Navier–Stokes equations with the Spalart–Allmaras improved delayed detached-eddy simulation model. A turbulent inlet boundary layer generation method is adopted to obtain more realistic inlet boundary conditions. First, uniform flow over a single cylinder at Re = 3900 and flow over a single cylinder above scoured beds at Re = 6000 were simulated to validate the numerical model, boundary layer generation method, and mesh density effect. Second, two cylinders in the tandem arrangement above scoured beds with six different pitch ratios L/D are investigated numerically in terms of instantaneous vortex characteristics, the hydrodynamic force, and time-averaged flow fields. The simulation results in scoured beds are compared with simulations under the near flat wall and wall-free conditions. The major findings can be summarized as follows. (1) When L/D≤2.0, the wake of two tandem cylinders is dominated by the intermittent shedding, and the downstream sand dune in the scoured bed hinders the Kármán vortex formation at the rear of the downstream cylinder. Lift force fluctuations of the two cylinders have small amplitudes, and their spectra show a multi-peak distribution and no dominant peak frequency in the spectrum of the upstream cylinder. A squarish cavity-like recirculation zone is formed between two cylinders at L/D=2.0. (2) When L/D≥3.0, the periodic vortex shedding is evident in the wake of the upstream cylinder, and the small sand berm between two cylinders has an impact on the bottom shear layer of the upstream cylinder. The downstream cylinder is periodically impacted by the vortices shed from the upstream cylinder. Lift force spectra of the upstream and downstream cylinders have the same peak frequency. (3) Due to the influence of scoured bed and the inlet boundary layer, the time-averaged lift coefficient of the upstream cylinder remains negative when L/D≥1.5, and the critical spacing for drag inversion is relatively smaller compared with under wall-free conditions. The negative pressure coefficient values of the upstream cylinder are smaller than the values in near flat wall and wall-free conditions.

Direct numerical simulations of aerodynamic performance of wind turbine aerofoil by considering the blades active vibrations

In the present study, the aerodynamic performance of the horizontal-axis wind turbine blades by considering the flap-wise oscillations are numerically investigated by using direct numerical simulations (DNS). The details of flow structure can be analysed and predicted by performing DNS over an oscillating blade by considering the realistic behaviour of the wind turbine blade structure with natural vibration frequencies. In this study, the impact of vibrations on the flow separation point, laminar separation bubble (LSB) and stall over NACA-4412 aerofoil are investigated utilising the high-fidelity spectral-hp element methodology. The Reynolds number and angle of attack were selected in the range of 50,000≤Re≤75,000 and 8°≤AoA≤16°. It is found that the blade vibrations have a noticeable impact on the aerodynamic performance and delay the stall occurrence, and the lift remains high even at higher AoAs, in comparison with the stationary blade. The size of the flow separation is reduced by the blade oscillation and the vibration also affects the separation point. Due to the harmonic oscillation of the blade, the pressure signals are periodic, and the pressure fluctuations are amplified by the oscillations, especially in the flow separation region. The time-averaged lift coefficient is increased by 255.3% by raising the angle of attack, from 0° to 12° at Re = 75,000. Compared to Re = 50,000, the peak-to-peak amplitude for the angle of attack of 0° is higher, whereas that of 8° and 12° are slightly lower at Re = 75,000.

An LBM-based investigation of thermal buoyancy and arrangement angle on flow characteristics and heat transfer over four heated square cylinders

In this work, the effects of thermal buoyancy and rotation angle on the hydrodynamics and mixed convection heat transfer characteristics over four heated identical square cylinders placed in a parallel horizontal channel are numerically studied. For the flow field, the Lattice Boltzmann method (LBM) with multiple relaxation time collision operator (MRT) is implemented and the Bhatnagar-Gross-Ktook collision operator (BGK) is adopted for the thermal field simulation. The distance between two adjacent square cylinders is fixed for a parametric study and a uniform velocity is imposed at the inlet region. Ranges of the influence parameters are defined as: α = 45°, 90°, 120°; 50 ≤ Re ≤ 150; 0 ≤ Ri ≤ 0.5. Several flow and heat transfer parameters including the time-averaged lift/drag coefficients, the global time-averaged Nusselt number and the distributions of local Nusselt number are analyzed, respectively. The vorticity and isotherm patterns are also plotted to illustrate the visual disturbance of the thermal buoyancy and the rotation angle on the flow and thermal fields. Numerical results show that the flow and thermal patterns for all arrangements become disordered and nonsystematic with the introduction of thermal buoyancy, and the thermal pattern for the downstream cylinders has an upward drift in the wake region. The time-averaged lift coefficient for each square cylinder is relatively sensitive to the influence parameters and the arrangement, and it is always less than zero when the Richardson number is not equal to zero. The global time-averaged Nusselt number is directly proportional to the Reynolds number and Richardson number, and the local Nusselt numbers on the front and rear faces for each square cylinder reach a maximum and minimum, respectively. It is also observed that the distribution of local Nusselt number for all rotation angles is intensively affected by the thermal buoyancy.

Numerical investigation of unsteady flow across tandem square cylinders near a moving wall at Re = 100

Flow across tandem square cylinders placed close to a plane moving wall, has been studied extensively for various cylinder inter-spacing ratio (0.5≤S/D≤8) and cylinder-to-wall gap ratio values (0.1≤G/D≤4) at a fixed value of Reynolds number, Re = 100. Numerical experiments are performed using the computational package ANSYS FLUENT®. Results indicate that unsteady flow past tandem cylinders relies primarily on the presence of a moving wall. Exhaustive details on the effects of varying S/D and G/D values on the onset and suppression of vortex shedding behind the tandem cylinders are given. A detailed description of the underlying flow physics is provided through instantaneous vorticity and streamline contours. Forces such as the lift and drag acting on the cylinders are reasoned qualitatively through time-averaged pressure, lift, and drag coefficient plots. A remark on existence and suppression of flow unsteadiness is given through Strouhal number variation. A rigorous comparison of the present flow field with flow past an isolated square cylinder, square cylinder near a moving wall, and unbounded tandem cylinders is given. Overall, unlike the lift, drag coefficient values happen to be highest for single cylinder case, followed by the upstream cylinder, and they are least for the downstream cylinder.

Study on the hydrodynamic characteristics of a marine riser under periodic pulsation disturbance

In this paper, the hydrodynamic forces and vortex distributions of a riser subjected to a non-uniform flow generated by an upstream oscillating wing structure are simulated using high-precision code Incompact3d combined with immersed boundary method. The effects of in-line and transverse positions, oscillating frequency and amplitude on riser performance have also been discussed. It is found that with the increase of in-line spacing or the decrease of oscillation frequency and transverse positions, the time-averaged drag coefficient of riser changes from the negative values to positive values. The time-averaged lift coefficient of riser is generally insensitive to oscillation frequency. However, it shows a large shift when changing the transverse positions or the amplitude of the wing is larger than π/6. Moreover, for various in-line positions, oscillating frequency and amplitude, the vortex shedding of the rigid riser, indicated by the main frequency of lift force, is always locked by the oscillating wing. However, when the transverse position is changing, the ratio of main frequency of lift coefficient to the swing frequency does not still remain 1:1. More concretely, the maximum time-averaged drag coefficient and lift coefficient Root-mean-square value of 0.559 and 1.629 is obtained in the simulation respectively.

LES investigation on vortex dynamics of transient sheet/cloud cavitating flow using different vortex identification methods

The sheet/cloud cavitating flow always contains complex multiscale vortex structures generated by the cavity cloud shedding and collapsing. In this study, the transient sheet/cloud cavitating flow around a Clark-Y hydrofoil is numerically investigated using the Large Eddy Simulation (LES) method coupled with the Zwart–Gerber–Belamri (ZGB) cavitation model. The simulation accurately reproduces the unsteady cavitation evolution process, and the predicted time-averaged lift and drag coefficients, total vapor volume variation and velocity distribution agree fairly well with the experimental measurements. The cavitation vortex dynamics are studied in detail with different vortex identification methods including the vorticity method, the [Formula: see text]-criterion method, the [Formula: see text] method, the [Formula: see text] method and the Liutex method. The vortex identification ability of the different methods in the transient sheet/cloud cavitating flow is also discussed. Generally, the Liutex method combines the advantages of the other methods and can accurately identify both the vortex position and strength. Further analysis of cavitation-vortex interactions demonstrates that the cavity cloud shedding and collapsing have a pronounced influence on the vortex structure.

Evaluation of vorticity forces in thermo-sensitive cavitating flow considering the local compressibility

The correlation between hydrodynamic forces and cavity evolution has been widely investigated but has not been deeply revealed. This study uses force element method to analyse the characteristics of force evolution along with cavitation around a NACA0015 hydrofoil. A modeling framework using the mixture two-phase flow model considering the energy convection and compressibility is proposed, to investigate the compressibility and thermal effects in the thermo-sensitive cavitating flow. Moreover, a force element method is applied for evaluating vorticity forces. The evolution of lift and drag coefficients under different cavitation numbers is mainly studied. Results indicate that, with increasing cavitation number, the time-averaged lift and drag coefficients firstly rise and then decline. However, the drag coefficient decline trend is greater than the lift coefficient. Combined with cavity evolution, the transient lift and drag evolution is analysed. Positive lift elements are mainly concentrates on the cavity surface and transport with cavity development, but the rupture of detached cavity and the pressure wave will inhibit the growth. The lift force reaches its peak when the cavity forms with the attached cavity that is completely detached from the hydrofoil surface, because of the volume of positive lift element reaches its maximum. Except for the shearing fracture of leading edge with the effect of fluid impact, the evolution of drag elements is similar to the lift. This studies shows that the force element method can well reveal the mechanism of force evolution due to the cavitation.

Pulsed Jet Characteristics of Circulation Control Airfoil

Compared with the steady jet, the mass flow consumed by the pulsed jet is lower, which is of great significance for solving the jet source in the circulation control technology. In order to further study the effects of different parameters on energy consumption and aerodynamic coefficient pulse in pulsed jet, based on the Reynolds average N-S equation, the aerodynamic characteristic calculation and flow field analysis of the circulation control airfoil under the action of pulsed jet are carried out, and the aerodynamic benefit is evaluated with the combination of energy consumption and aerodynamic coefficient fluctuation. The results show that: Pulsed jet is more suitable for use at high angle of attack. By using the combination of pulsed jet and steady jet, good results can be obtained in three aspects: time-averaged lift coefficient, lift coefficient fluctuation and energy consumption. The research results can be used as a reference for guiding the use of pulsed jet in circulation control technology.

Numerical study on characteristics of flow and thermal fields around rotating cylinder

In this paper, a numerical simulation has been performed to study the fluid flow and heat transfer around a rotating circular cylinder over low Reynolds numbers. Here, the Reynolds number is 200, and the values of rotation rates (α) are varied within the range of 0 &lt; α &lt; 6. Two-dimensional and unsteady mass continuity, momentum, and energy equations have been discretized using the finite volume method. SIMPLE algorithm has been applied for solving the pressure linked equations. The effect of rotation rates (α) on fluid flow and heat transfer were investigated numerically. Also, time-averaged (lift and drag coefficients and Nusselt number) results were obtained and compared with the literature data. A good agreement was obtained for both the local and averaged values.

Kinematic parameter optimization of a flapping ellipsoid wing based on the data-informed self-adaptive quasi-steady model

This paper constructs an optimization framework based on the data-informed self-adaptive quasi-steady model. The framework aims at achieving a specific aerodynamic force coefficient by optimizing the kinematic parameters of the flapping motion of an ellipsoid wing. All the model coefficients of this quasi-steady model are calibrated empirically by the data-informed training. At each optimization iteration, the data-informed training is implemented by the local ridge regression, where the initial training samples are extracted from simulation examples, and the weight coefficients are calculated by the compactly supported radial basis function with the previous optimal solution as the center point. Furthermore, a numerical simulation is conducted to evaluate the accurate aerodynamic force coefficient corresponding to the current optimal solution. The relative error between the accurate simulation result and optimization objective is calculated as the convergence criteria of the optimization. Then, the effects of the kinematic parameters on the time-averaged lift coefficient are first investigated, which indicate that the in-phase flapping with high flapping angle amplitude and medium geometric angle of attack amplitude is beneficial to the lift coefficient. Moreover, the kinematic optimization is conducted for a three-dimensional flapping ellipsoid wing in the hovering mode. The results demonstrate that the leading-edge vortex is crucial for the force generation. Moreover, in one flapping period, the asymmetrical wake and two unequal lift coefficient peaks emerge under the figure-O motion pattern while the vortex structures are highly symmetrical under the figure-8 motion pattern.

Effect of Turbulence and Sinusoidal Pitching on Low-Reynolds-Number Lift

Small fixed-wing unmanned aerial vehicles (UAVs) are becoming increasingly popular in civil and military use. However, their ability to fly in adverse weather and turbulent flows is hindered by their low-Reynolds-number wings. It is shown that turbulence produces a significant pitching flow, as observed by the wing, which raises the possibility of intermittent dynamic stall comparable to a pitching airfoil situation. Two airfoils (one symmetrical and the other cambered) were tested in the wind tunnel at Reynolds numbers relevant to small UAVs: between 50,000 and 200,000. Two turbulence intensities of 5 and 15% were compared to sinusoidal pitching of the airfoils at equivalent amplitudes and three frequencies. It is shown that an increase in either the pitch amplitude or the onset turbulence intensity produces comparable changes in the time-averaged lift coefficient, and both experience forms of dynamic stall. The transient behavior is, however, significantly different; and the airfoil form has greater influence on the response to pitching motion than to turbulent flow.

Influence of wake confinement and buoyancy on flow past a square cylinder

A study of vortex shedding from a square cylinder with wake confinement is carried out for the gap ratio (G/D) in the range 0.1–12.0 for 30 ≤ Re ≤ 150. Wake confinement is achieved by placing the cylinder near a moving wall. The critical Reynolds number (Recr) for the onset of vortex shedding first decreases and then increases with a decrease in the gap-ratio. The influence of mean velocity in the gap and shear-layer formed on the moving wall during the transition of wake from steady to an unsteady state are investigated. In contrast to the case of a stationary wall, vortex shedding in the present case is observed even for quite low values of the gap ratio (G/D = 0.1). It is observed that the destabilization tendency of flow increases for G/D > 0.3. The influence of buoyancy on the vortex shedding for the given configuration is also examined for 0.1 ≤ G/D ≤ 1 and for −1 ≤ Ri ≤ 1, where buoyancy effects are introduced by heating or cooling the cylinder. Unlike the case of a stationary wall, dual roles of buoyancy have been observed. It acts as a stabilizing mechanism at low gap ratios while it destabilizes the flow at large gap ratios. Further, the influence of baroclinic production of vorticity on the flow is investigated. In the gap region, it is positive for Ri > 0 and negative for Ri < 0. Streamlines, vorticity and temperature contours and Nusselt number for different values of G/D, Re and Ri are presented. It was observed that the time-averaged drag coefficient increased with Ri and the time-averaged lift coefficient decreased with Ri except for G/D = 0.1. For G/D = 0.1, the time-averaged lift coefficient was found to increase with Ri.

Wake Modifications in Confined Flows Due to the Presence of a Downstream Cylinder in Staggered Arrangement

In the present study, confined flows around two square cylinders in staggered arrangement were numerically investigated. Cross-flow and streamwise center-to-center spacings of one- and three-cylinder diameters, respectively, were considered. Simulations were carried out at Reynolds numbers Re = 50,100,150 and 180, where the resulting wakes are laminar and periodic. Results indicate that the presence of the downstream cylinder tends to reduce the Strouhal number, amplitude and the time-averaged lift coefficient of the upstream cylinder relative to the single cylinder cases. Furthermore, the time variations of upstream cylinder’s lift coefficient behave similar to that of a single cylinder.