Mean Lift Coefficient Research Articles

Numerical investigation on the end effects of the flow past a finite rotating circular cylinder with two free ends

This paper studies the impact of the aspect ratio and free end shape on the end effects in the flow past a rotating circular cylinder with two flat, radiused, hemispherical, and conical ends, using the large eddy simulation method at a Reynolds number of 4.6×104. The aspect ratio in the range of 6-30 and the rotation rate in the range of 0-3, are investigated. The results show that the mean drag coefficient initially decreases slightly before rapidly increasing with the rotation rate, with a critical rotation rate that rises from 1 to 1.5 as the aspect ratio increases from 6 to 30. In contrast, the mean lift coefficient increases with both the rotation rate and the aspect ratio. When the rotation rate increases and the aspect ratio decreases, the differences between the aerodynamic coefficients of the four end shapes become more pronounced. The flat end results in the highest mean drag and lift coefficients, while the hemispherical end yields the lowest ones. In addition, when the rotation rate increases, the alternate shedding vortices shift to the opposite side. They even disappear and increase the elongated streamwise vortices. Due to the combined impacts of the rotation and end effects, large-scale tip vortices are formed, significantly altering the wake structure. The intense rotation effect results in expanding the strong influence region of the end effects and shrinking (or even removing) the weak influence region.

Numerical simulations on cables attached with different shapes of lights and its mitigations by using perforated shrouds

To reduce the cable vibration caused by rectangular lights, the light shape is modified to be ellipsoidal and circular sections, together with the use of a perforated shroud. Numerical simulations on six types of cable-light models were conducted using computational fluid dynamics. The mean drag coefficient CD, mean and mean lift coefficient CL, mean of the ellipsoidal lights, circle lights, and perforated shroud cable are reduced compared to the rectangular light. CD, mean can be reduced by a maximum of 50%; CL, mean can be reduced by a maximum of 43%. The maximum fluctuating drag and lift coefficient are also significantly reduced. This indicates that the perforated shrouds might be useful to mitigate the vortex-induced vibration. The ellipsoidal and circular lights are significantly better than rectangular lights in terms of galloping critical wind speed. Furthermore, the perforated shroud is very beneficial for suppressing galloping vibration. The variation of Strouhal number St with the wind attack angle for the shroud rectangular light cable model is relatively smooth, all around 0.1. The wake vortices of rectangular light, ellipsoidal light, and circular light are shed alternately in a typical 2S pattern. However, the alternately shedding vortex of the shroud cable was interrupted by the flow of air through the holes. When the wind attack angle exceeds the most dangerous wind attack angle, the incoming stream cannot be reattached after separation, and the force on the cable is greatly reduced, resulting in a sudden drop in the average lift coefficient. Wind pressure in the gap between the shroud and the cable is negative. The fluctuating wind pressure coefficients on the shrouded cables are significantly lower than those of rectangular lights because of the interference effect of the outer perforated shrouds. In total, the perforated shroud is the best to reduce the galloping caused by the rectangular light.

Dynamics and Wake Interference Mechanism of Long Flexible Circular Cylinders in Side-by-Side Arrangements

The vortex-induced vibrations of two side-by-side flexible cylinders in a uniform flow were studied using a three-dimensional direct numerical simulation at Reynolds number Re = 350 with an aspect ratio of 100, and a center-to-center spacing ratio of 2.5. A mixture of standing-traveling wave pattern was induced in the in-line (IL) vibration, while the cross-flow (CF) vibration displayed a standing-wave characteristic. The ninth vibration mode prominently occurred in both IL and CF directions, along with competition between multiple modes. Proximity effects from the neighboring cylinder caused the primary frequency to be consistent between IL and CF vibrations for each cylinder, deviating from the IL to CF ratio of 2:1 in isolated cylinder conditions. Repulsive mean lift coefficients were observed in both stationary and vibrating conditions for the two cylinders due to asymmetrical vortex shedding in this small gap. Comparatively, lift and drag coefficients were notably increased in the vibrating condition, albeit with a lower vortex shedding frequency. Positive energy transfer was predominantly excited along the span via vortex shedding from the cylinder itself and the neighboring one, leading to increasing lower-mode vibration amplitudes. The flip-flopping (FF) wake pattern was excited in the stationary and vibrating cylinders, causing spanwise vortex dislocations and wake transition over time, with the FF pattern being more regular in the stationary cylinder case.

Wake Structures and Hydrodynamic Characteristics of Flows around Two Near-Wall Cylinders in Tandem and Parallel Arrangements

To clarify the hydrodynamic interference characteristics of flows around multiple cylinders under the wall effect, the two-dimensional (2D) flows around the near-wall single, two tandem and parallel cylinders are simulated under different gap ratios (0.15 ≤ G/D ≤ 3.0) and spacing ratios (1.5 ≤ T/D ≤ 4.0) at a Reynolds number of Re = 6300. We also examine the wake patterns, the force coefficients, and the vortex-shedding frequency with emphases on the wall effect and effects of the two-cylinder interference. A critical wall gap of G/D = 0.6 is identified in the single-cylinder case where the wall can exert significant influences. The two near-wall tandem cylinders exhibit three wake states: stretching mode, attachment mode, and impinging mode. The force coefficients on the upstream cylinder are significantly affected by the wall for G/D ≤ 0.6. The downstream cylinder is mainly influenced by the upstream cylinder. For G/D > 0.6, the force coefficients on the two cylinders exhibit a similar variation trend. In the parallel arrangement, the two cylinders exhibit four wake states in different G/D and T/D ranges: double stretching mode, hetero-vortex scale mode, unilateral vortex mode, and free vortex mode. Moreover, the two parallel cylinders in the hetero-vortex scale or free vortex mode have two states: synchronous in-phase state and synchronous out-of-phase state. The mean drag coefficients on the two cylinders decrease, while the mean lift coefficients exhibit opposite variation trends, as the T/D grows.

Proximity to the water surface markedly enhances the force production on underwater flapping wings.

The potential application of flapping wings in micro-aerial vehicles is gaining interest due to their ability to generate high lift even in confined spaces. Most studies in the past have investigated hovering wings as well as those flapping near solid surfaces. However, the presence of surface tension at the water-air interface and the ability of the water surface to move might differentiate its response to the proximity of wings, compared to that of solid surfaces. Motivated by underwater, amphibian robots and several underwater experimental studies on flapping wings, our study investigated the effects of the proximity of flapping wings to the water surface at low Reynolds numbers (Re = 3400). Experiments were performed on a rectangular wing in a water tank with prescribed flapping kinematics and the aerodynamic forces were measured. The effects of surface proximity on the wing in its both upright and inverted orientations were studied. Broadly, the mean lift and drag coefficients in both orientations decreased significantly (by up to 60%) as the distance from the water surface was increased. In the case of the upright orientation, the mean lift coefficient was slightly decreased very close to the water surface with its peak being observed at the normalized clearance of [Formula: see text]. Overall, the study revealed an enhancement in the aerodynamic forces closer to the water surface.

Effect of Prandtl number and free-stream orientation on global parameters for flow past a heated square cylinder

In this study, an in-depth examination of the aerodynamic parameters involving forced and mixed convection around a heated square cylinder is presented. The ranges of Prandtl number (Pr), Richardson number (Ri), and flow orientation (α) are kept as 0.71 ≤ Pr ≤ 1000, 0 ≤ Ri ≤ 1.6, 0° ≤ α ≤ 90°, while the Reynolds number (Re) and the cylinder orientation (ϕ) are kept fixed as Re = 100 and ϕ = 0°, respectively. The flow is considered as two-dimensional (2D), steady, laminar, incompressible, and viscous. The buoyancy effects are taken into account through the Boussinesq approximation. At lower Pr, the flow shifts from unsteady to steady with increasing Ri. This transition persists at higher Ri with increasing Prandtl values. The flow remains consistently unsteady at α = 90°. Isotherm crowding intensifies with higher Pr and/or Ri across all flow inclinations. Across the complete spectrum of flow angles, it is noted that the mean lift coefficient rises as the Richardson number increases. Additionally, the mean drag coefficient reaches its peak at Ri = 1.6 when Pr = 0.71. The findings reveal that the Strouhal number (St) rises as the Richardson number (Ri) increases, and it decreases as the Prandtl number (Pr) increases. The mean Nusselt number (Nu¯) demonstrates an upward trend as the Prandtl number increases, with Ri held constant. It is also observed that Nu¯ is more sensitive to the Prandtl number than the Richardson number and is maximum at Pr = 1000 for the selected range of flow orientations.

Reynolds-number scaling analysis on lift generation of a flapping and passive rotating wing with an inhomogeneous mass distribution

Insects usually fly by passively rotating wings, which has been applied to the design of flapping-wing Micro-Air Vehicles (MAVs) to reduce mechanical complexity. In this paper, a robotic passive rotating-wing model is designed to investigate wing kinematics and lift generation, which are measured by a high-speed camera and a force transducer, respectively. In addition, flow fields are measured using the Particle Image Velocimetry (PIV). Experimental results demonstrate that passive rotating motion has a coordinative relationship with actively stroking motion. As the stroke amplitude or frequency increases, the rotating amplitude is enlarged. To characterize the active stroking motion, a driving Reynolds number Redriving is defined, which varies from 68 to 366 in this study. Moving the gravity center of the wing towards trailing edge induces the increase of additional torque M, which decreases the wing rotating amplitude and promotes the advance of wing rotation. We find that the timing of wing rotation is gradually delayed and the mean lift coefficient CL¯ monotonously decreases as Redriving increases. By increasing the additional torque M, CL¯ is slightly improved and approaches to the lift coefficient of a real fruit fly at driving Re approximately equal to 230. The instantaneous lifts combined with the vortical structures further demonstrate that the lift generation associated with wing rotation is mainly attributed to the growth of the Leading-Edge Vortex (LEV) and the passive wake capture mechanism. Passive wake capture is influenced by LEV, reversal stroke motion and wing additional torque together, which can only maintain the lift at a high level for a considerable period. The high-lift generation mechanisms of flapping and passive rotating flight could shed light on the simplified design of MAVs and the improvement of their aerodynamic performance.

Effect of Gurney Flap on the Aerodynamic Performance of a Flapping Foil: Micro-Aerial Vehicle Application

Abstract Even with its small size, the Gurney flap (GF) can help considerably in increasing the lift of foils and wings. To exploit this feature, the objective of this research was to numerically study the effects of this flow control device on the aerodynamic performance of oscillating foils for micro-aerial vehicle (MAV) applications. Three sets of each important parameter were selected: the height (0.01c, 0.04c, and 0.16c), angle (45 deg, 90 deg, and 135 deg) and location from trailing edge (T.E, 0.05c and 0.1c). A two-dimensional laminar, incompressible Navier–Stokes equation solver was used to computationally investigate the effect of the Gurney flap on the aerodynamic performance of a flat plate (chord length = 10 mm and thickness = 0.03c). It was found that the best aerodynamic performance was obtained when the Gurney flap was installed at the trailing edge with a height of 0.04c and mount angle of 90 deg. The height of the Gurney flap had a major impact on aerodynamic performance. Results showed an increase of 23.5% in mean lift coefficient, 15.5% in maximum lift coefficient, and 5% in power economy as compared to flat plate, which is accredited to the increase in effective camber and the formation of counter-rotating vortices, decreasing the adverse pressure gradient. The weakening of counter-rotating vortices downstream of Gurney flap could also be the contributing factor to its good performance. The results suggest that the Gurney flap may be useful in enhancing the performance of wings for bio-inspired flapping wing MAVs.

A novel vortex-induced vibration model for a circular cylinder in the vicinity of a plane wall

A novel vortex-induced vibration (VIV) model is proposed to predict the transverse responses of an elastically mounted circular cylinder in the proximity of the wall. Firstly, flow characteristics and hydrodynamic loads on a near-wall stationary circular cylinder are summarized and analyzed based on the existing experimental results, and then the Strouhal shedding frequency and the empirical correlations of the mean lift coefficient and oscillating lift coefficient are established. Subsequently, by introducing the empirical correlations of fluid loads to the equations of structure vibration, a novel VIV model for the near-wall circular cylinder is proposed to describe more precisely the effect of the plane wall. The accuracy, stability, and adaptability are validated by employing experimental VIV results. Compared to existing models, the novel model has advantages in achieving acceptable accuracy in various scenarios. Finally, using the proposed VIV model, the dynamic features of a near-wall circular cylinder to the reduced velocity and gap ratio are studied in detail, including the time-averaged displacements, lock-in regime, maximum amplitude, and dominant frequency. The results obtained are valuable for understanding the VIV characteristics of the near-wall cylinder, and the semi-empirical VIV model proposed could be applied in engineering prediction in the future.

Discrete integration for measuring aerodynamic loads on trains in crosswinds − realizable strategies of discretization and discrete integration

Discrete integration occupies an important place in train aerodynamic tests in crosswinds. Improved delayed detached eddy simulations based on shear stress transport k-ω turbulence models were carried out to calculate the side force, lift, rolling moment around the lee rail, and surface pressure on bluff and streamlined vehicles. The changepoints and piecewise linearities of the pressure coefficients were evaluated, and the maximum coefficient of determination in the elements was 0.9973. A realizable strategy of the discretization based on the Lagrange rectangular elements was suggested, including the largest lengths and numbers of the elements. From this, a strategy of the discrete integration was presented to measure the aerodynamic loads, considering the real orientation of the elements. The maximum errors of the mean aerodynamic load coefficients of the bluff and streamlined vehicles were 4.1% and 2.2% (except the mean lift coefficient of the bluff vehicle), respectively. The errors were less than those in the previous studies, especially for the streamlined vehicle, which reduced by up to 8.7%. The unsteady aerodynamic loads with no delay obtained by the strategies were near to natural ones in the frequency range that people would be concerned about in crosswinds (at the Strouhal number of less than 0.4). Some suggestions were made for using the strategies in the full-scale tests and model tests, which provided a foundation for further studies of the running safety in natural crosswinds.

Investigations on vortex evolution and wake dynamics of bio-inspired pitching hydrofoils

Recently, lots of oscillating targets inspired from motions of some insects and birds have been applied extensively to many engineering applications. The aim of this work is to reveal the performance and detailed flow structures over the pitching corrugated hydrofoils under various working conditions, using the SST [Formula: see text] transition model. First of all, the lift coefficients of a smooth oscillating airfoil at different reduced frequency and pitching angles show a good agreement with the experiments, characterized by the accurate prediction of the light and deep stall. For the pitching corrugated hydrofoils, it shows that the mean lift coefficient increases with the pitching magnitude, but it has an obvious drop at high reduced frequency for the case with large pitching amplitude, which is mainly induced by the pressure modification on the surface with smooth curvature, depending on the oscillation significantly. In addition, the mean drag coefficient also indicates that the drag turns into the thrust at high reduced frequency when the pitching amplitude exceeds to the value of 10°. Increasing the reduced frequency delays the flow structure and leads to the deflection of the wake vortical flow. The Reynolds number also has an impact on the hydrofoil performance and wake morphology. Furthermore, regarding the shape effect, it seems that hydrofoil A (consisting of two protrusions and hollows and the aft part with smooth curvature) achieves the higher lift than hydrofoil B (comprising several protrusions and hollows along the surface), specially at high reduced frequency. Although the frequency collected from two hydrofoils remains nearly the same near the leading edge and in the wake region, the high sub-frequency is evidently reduced for hydrofoil B in second and third hollows, due to the relatively stable trapped vortices. Then, the wake transition from the thrust-indicative to drag-indicative profile for hydrofoil B is also slower compared with hydrofoil A. Finally, it is observed that with the increase of the thickness, the lift/drag ratio decreases and the slow wake transition is detected for the thin hydrofoil, which is associated with the relatively low drag coefficient.

Effect of Gap and Diameter Ratio on Vortex-induced Forces for Cylinders in Tandem at Re=100

Abstract The article investigates fluctuations of the vortex-induced loads related to the effects of gap and diameter ratio on the mean drag and lift coefficients of the downstream cylinder, when two circular stationary cylinders of different diameters are arranged in a tandem configuration. The study is performed with the method of computational fluid dynamics for the low Reynolds number of 100. The benchmarking of the numerical model is followed by the parametric investigation with the variation of: a) the ratio of diameters of the upstream to downstream cylinder (d/D), in order to observe the effects associated with relative sizes of structures; b) the gap-to-diameter ratio (G/D), in order to observe the combined effects of varying these geometrical quantities. The results demonstrate a rapid change in the mean drag and lift coefficient values at the gap-to-diameter ratio between 2.0 and 3.0 at the diameter ratios of 0.7 and 1.0.

Numerical study of three-dimensional flapping wings hovering in ultra-low-density atmosphere

This paper presents a numerical study on the aerodynamic performance of three-dimensional flapping wings hovering in ultra-low-density fluid by using an immersed boundary method with a focus on the effects of compressibility on force production and flapping efficiency. Simulations are conducted by varying Mach number, aspect ratio, stroke amplitude, and flexibility of the wing. It is found that the lift coefficient and efficiency of rigid wings are reduced by up to 10.6% and 10.7%, respectively, when the Mach number is increased from 0.2 (weakly compressible) to 0.9 (highly compressible). To achieve sufficient lift force in the ultra-low-density atmosphere, three main strategies including varying the aspect ratio, stroke amplitude, and flexibility of wings are explored. It is found that a wing with high aspect ratio, small and fast stroke motion, and moderate flexibility is able to generate a high lift. An optimized flexible wing according to the aforementioned analysis is further proposed and simulated, which shows 38.3% and 20.8% enhancements of the mean lift coefficient and efficiency, respectively. The present study shows that the flapping aerial vehicle in ultra-low-density atmosphere is highly feasible from the aerodynamic point of view.

Vortex-induced vibrations of flexible cylinders predicted by wake oscillator model with random components of mean drag coefficient and lift coefficient

In the present study, vortex-induced vibrations in both In-Line and Cross-Flow directions of long flexible cylinders within a uniform flow are predicted by a modified wake oscillator model. In detail, the Van der Pol's wake oscillator model with the drag and lift coefficients being modelled as random variables. The statistics of the force coefficient, i.e. mean value and standard deviation, are extracted from the literature reporting experimental measurements and numerical simulation results of the drag and lift forces experienced by the cylinder-type structure. With the statistics, a series of pseudo stochastic variables are generated to calculate the drag and lift forces. In Euler-Bernoulli equation governing the motion of the cylinder, tension is modelled as a function of flow velocity. Through comparing the predictions from the model with and without randomness to the experimental results, it is found that the scatter in vibration amplitudes, multi-frequency effect (broadband stochastic process) and frequency multiplication effect are successfully reproduced by the model with randomly drawn drag and lift coefficients. However, the overestimate of the oscillation frequency for the In-Line vibrations implies that the In-Line coupling is still a topic that deserves a further investigation.

Pressure and force measurement-based investigations on aerodynamic characteristics of a trapezoidal section

Trapezoidal cross-section with overhangs/lateral cantilevers are being increasingly adopted for medium span cable stayed bridges. Wind tunnel investigations have been carried out to study the aerodynamic characteristics of a trapezoidal section using pressure and force measurement. Simultaneous measurement of fluctuating pressures and overall forces have been carried out under uniform, smooth inflow low for various angles of wind incidence, in the range of −15° and 15° at a wind speed of 12.6 m/s. The variation of mean and fluctuating components of aerodynamic coefficients, viz, drag, lift and torsional moment coefficients with angle of wind incidence have been presented. It has been observed that the mean aerodynamic coefficients evaluated using pressure measurement and force measurement are comparable. From the slope reversal of mean lift coefficient and occurrence of maximum value of mean lift coefficient, the critical angle of wind incidence has been identified as + 6°. Further, it has been observed that the trapezoidal section is stable against transverse galloping and torsional galloping on the basis of quasi-steady assumption.

Numerical Study of Local Scour around a Submarine Pipeline with a Spoiler Using a Symmetry Boundary Condition

A two-dimensional numerical model for solving the Navier–Stokes equations was developed to investigate the local scour around a submarine pipeline with a spoiler. Both the suspended load and the bed load were considered in the present numerical model. The focus of the present study is to investigate the effects of the spoiler length on the hydrodynamic forces on the pipeline and the spoiler as well as the local scour around the submarine pipeline. The corresponding numerical results show that the mean drag coefficients of the pipeline and the spoiler increase with the increase of the spoiler length. As for the mean lift coefficient, a general decreasing trend with the increasing spoiler length is observed for the pipeline. However, the mean lift coefficient of the spoiler first increases and then decreases with the increasing spoiler length. In addition, it is found that a larger spoiler length leads to a deeper scour depth, and an empirical equation was proposed for predicting the non-dimensional scour depth of submarine pipelines with non-dimensional spoiler length based on the numerical results.

Large eddy simulation of incident flows around polygonal cylinders

In this study, we carry out large eddy simulation of incident flow around polygonal cylinders of side number N=5−8 at Reynolds number Re=104. In total, six incidence angles (α) are studied on each cylinder ranging from face to corner orientations, thus covering the entire α spectrum. Special focus is put on the time-mean aerodynamic forces including lift, drag, and vortex shedding frequencies as well as the near wake flow features. It is found that because of y-plane asymmetry of polygonal cross sections at most incidence angles, the flow separation characteristics and hence the induced base pressure distribution and the aerodynamic forces exhibit unique and complex dependence on α and N. While the general inverse relation of drag coefficient and Strouhal number previously proposed from experimental observations at principal orientations still holds at arbitrary α, the variation of the two is found to be non-monotonic on both α and N. We also found that compared to the absolute time mean shear layer length measured from the final separation point, the extent of them stretched to the wake, measured from the cylinder center, is a powerful scaling factor for all the quantities investigated, including the wake characteristic length scales. In particular, the difference between the top and the bottom shear layer (due to geometrical asymmetry at arbitrary α) describes the variation of the non-zero time mean lift coefficient reasonably well, whose sign varies with N non-monotonically.

Effect of cable surface geometry and ice accretion shapes on the aerodynamic behaviour of inclined stay cables

A wind-tunnel study has been conducted to evaluate changes in the aerodynamic behaviour of stay cables of a bridge due to ice accretion from freezing rain and, due to different cable surface geometries. Numerical simulations were performed to predict the three-dimensional ice shapes resulting from freezing rain for a variation of environmental conditions: wind speed, wind direction, air temperature, velocity of precipitation and duration of precipitation. Stay-cable models were fabricated using laser selective sintering for three different surface geometries (double helical fillet, concentric rings, and double helical strakes) with ice formed under the same environmental conditions. Additional models with the helical fillet geometry were fabricated to evaluate the effect of the air temperature at which ice was formed, the effect of wind direction during the precipitation event and the effect of the duration of the precipitation. The aerodynamic drag and lift forces acting on the models were measured for different wind speeds and cable-wind angles. The overall study evaluated the mean aerodynamic force coefficients of ten models in smooth flow, and two of the models were also tested in turbulent flow. The critical Reynolds number regime for the models of stay cable with ice accretion shapes occurred at a lower Reynolds number (below 100,000) than for the un-iced cables and the drag coefficient was less sensitive to increases in Reynolds numbers than the equivalent un-iced cables. These effects were attributed to the combined role of the ice-shape in determining the separation point combined with the higher surface roughness of the ice. An important observation was that for the three surface geometries and the range of test conditions that were considered, the maximum drag coefficients for ice-accreted models ranged from approximately 1.1 to 1.3, and were up to 50% greater than those observed without ice. The model with helical strakes and ice accretion exhibited the highest drag coefficient and exhibited more variation in lift coefficient with changes in Reynolds number than the other two cable surface geometries. The aerodynamic forces of an ice-accreted model followed similar trends in smooth and turbulent flow, but the drag coefficients were greater in turbulent flow. The presence and shape of the ice appeared to have a more dominant effect on the separation behaviour of the models than the presence of turbulence (for an ice-accreted model). The aerodynamic coefficients did not change greatly between the cases where ice was accreted at −0.5°C and −1.5°C due to the similar ice shape and thickness near the separation locations. The ice shape formed at −5°C was thicker but more localized and resulted in drag and lift coefficients that had greater variation with changes in the cable-wind plane. The effect of ice duration from 10 h to 20 h resulted in a increased variation in mean lift coefficient behaviour due to the asymmetric shape that resulted from the ice accretion parameters.

Effect of free-stream inclination and buoyancy on flow past a square cylinder in large-scale heating regime

The combined effects of free-stream inclination (α) and heating [ϵ=(Tw−T∞)/T∞] on aerodynamic and heat transfer parameters are studied at fixed Reynolds number (Re = 100), Prandtl number (Pr = 0.71), cylinder inclination (ϕ=0°), Froude number (Fr = 1.0), and Mach number (M = 0.1) in the large-scale heating regime. For this purpose, a non-Oberbeck–Boussinesq compressible model for thermally perfect gases incorporating volumetric straining as well as transport property variations under large-scale heating is employed. The free-stream inclination (α) is varied in the range [0°, 90°] while the over-heat ratio (ϵ) is varied in the range of [0, 1]. It is found that at small free-stream inclinations (α≤45°), increase in heating causes a significant increase in mean drag coefficient, while at large α (α>45°), heating has little effect on mean drag coefficient. The mean lift coefficient (CL) increases by increasing ϵ for any value of α except α = 0. At a fixed heating level, the variation of mean CL is very non-monotonic with lower values at α=45° and 90°. It is found that the increase in flow inclination from 0° to 90° reduces the sensitivity of Strouhal number (St) to heating. For ϵ≤0.6, mean Nusselt number exhibits a non-monotonic trend with increase in α and attains a maximum value at α ≅ 40°. However, for ϵ>0.6, heat transfer decreases with increase in α and is maximum for aligned flow (α=0°).

Large-eddy simulation of a full-scale underwater energy storage accumulator

Underwater energy storage provides an alternative to conventional underground, tank, and floating storage. This study presents an underwater energy storage accumulator concept and investigates the hydrodynamic characteristics of a full-scale 1000 m3 accumulator under different flow conditions. Numerical simulations are carried out using an LES turbulence model. Time-averaged and transient flow structures and force characteristics are analyzed. The results show that the vortex structures are complex and scale-rich, but periodic vortex shedding can still be identified. The shedding frequency is consistent with the fluctuation of the lift force in the cross-flow direction. A dominant Strouhal number of 0.18 is found. The mean drag and lift coefficients stabilize at 0.45 and 0.60, respectively, and are insensitive to Reynolds number variation. Modal analysis shows that the natural frequency of the accumulator falls between 27 and 48 Hz and is much higher than the vortex shedding frequency. Thus, for the accumulator model investigated in this study, the risk of vortex-induced vibration (VIV) fatigue damage is very low.