RMS Lift Coefficient Research Articles

Exploring synchronization and lift suppression in fluid flow around vibrating cylinder: a parallel CFD and global optimization investigation

In this study, we employ a parallel Computational Fluid Dynamics (CFD) code integrated with the VTDIRECT95 algorithm, a parallel deterministic global optimization method, to conduct global optimization for an oscillating circular cylinder. We conduct numerical simulations for the flow at a Reynolds number of 500 within the parameter range of 0.1≤Ax≤0.3 and 0.5fst≤fex≤2.5fst where Ax represents the inline oscillating amplitude, fex denotes the forcing oscillation frequency, and fst corresponds to the frequency of a stationary cylinder. To enhance computational efficiency, a combination of VTdirect and a CFD solver is utilized to efficiently identify the synchronization region, thereby reducing computational resources. The results reveal a significant reduction in the lift coefficient within the synchronized region compared to unsynchronized regimes. Furthermore, the study delves into the underlying flow physics behind synchronization and lift suppression. By synchronizing the shedding of vortices, their detrimental effects are nullified, resulting in a reduction in lift. Moreover, the research examines the influence of three-dimensional (3-D) flow by comparing 2-D and 3-D simulations at two different Reynolds numbers. It demonstrates that accounting for 3-D effects yields more accurate predictions of fluid behavior. Synchronization maps and root mean square (rms) lift coefficient plots illustrate the impact of Reynolds number and movement frequency on lift suppression. The findings indicate that achieving synchronization in 3-D flow necessitates stronger amplitudes and higher frequencies. At higher Reynolds numbers, the wake structures become unstable, leading to intricate vortical patterns. Consequently, the synchronization curve shifts towards higher amplitudes and frequencies in 3-D simulations. Understanding these phenomena is vital for reducing lift force in practical applications. This research significantly contributes to knowledge regarding synchronization and lift suppression in fluid flow around vibrating cylinders.

Numerical investigation of mixed convection from rectangular cylinders subjected to upper cross flow

Unsteady combined natural and forced convection heat transfer from a rectangular cylinder subjected to upward cross flow is investigated numerically. The working fluids are air (Pr = 0.7) and water (Pr = 7), and the flow is laminar. The governing flow and energy equations are solved using a fractional step finite-difference scheme. The effects of the cylinder aspect ratio (a = L/D), Reynolds and Richardson numbers on the flow and heat transfer characteristics are investigated. Numerical simulations were carried out for the cylinders with aspect ratios of a = 0.5, 1, and 2, while the Richardson and Reynolds numbers varied between 0 to 10, and 100 to 200, respectively. The mean drag, mean rms lift coefficients, as well as the Strouhal number and the mean Nusselt number were computed for each simulation to determine the quantitative effects on flow and heat transfer. Steady flow is observed for Pr = 0.7, Ri = 0.5, and a = 0.5 or for Re ≥ 150 and Ri ≥ 1. For Ri = 10 and Re = 200, the flow becomes unsteady in the downstream region and trigger vortex street formation for a = 0.5, 1, and 2. Decreasing the aspect ratio, as well as increasing Reynolds number, increases the heat transfer from the cylinder. The rms lift coefficient decreases sharply at Ri < 1 for Pr = 0.7, Ri < 2 for Pr = 7 due to vortex breakdown. Further increase in the Richardson leads to a slight increase in rms lift coefficient except for Re = 200 where the sharp increase is observed due to triggered vortex formation again. For air, the increase in the mean Nusselt number in Ri = 10 case with respect to the forced convection case (Ri = 0) was 54–65% and 80–98%, respectively, for a = 0.5 and 2, while these values for water were realized as 50–68% and 53–63%, respectively. Using the computed data and nonlinear regression, the mean Nusselt number and the drag coefficients were developed.

On the passive control of aeroacoustics noise behind a square cylinder

This study investigated the application of a splitter plate as a passive control method for reducing the aerodynamic sound of square cylinders. To control the noise and vortex shedding, the splitter plates attached to the downstream of the square cylinder have been used. The flow is assumed to be unsteady and it is simulated using the URANS equations model k-ω-SST. Aerodynamic noise calculations are carried out by the use of F-fowcs Williams-Hawkins analogy. To verify numerical results, the sound pressure level (SPL) obtained in different situations (Microphone position) is compared with the experimental results, and a good agreement is observed. The simulation is carried out with different lengths of the splitter, and the results can be divided into three groups besides the baseline configuration as well. In the first group, when the length of the splitter varies from 0.2 to 2D, noise is noticeably reduced by about 23 dB. In the second group, the length of the splitter increases from 3 to 5D, and the SPL is increased by about 42 dB. In the third group, the length of the splitter varies from 6 to 8D, which in turn the noise is decreased by about 4 dB (Compared to the second group). Results show that adding the splitter reduces the mean drag force generally. But the changes in the lift fluctuations are similar to the SPL variations. The results reveal that the optimal splitter length through which noise, RMS lift, and drag coefficients are reduced, occurs for a Splitter in the first category (i.e., L = 0.2–2D).

On the effect of temporal error in high-order simulations of unsteady flows

The present paper focuses on the effect that temporal error has on unsteady solutions modeled with a high-spatial-order, finite-element, streamline upwind/Petrov-Galerkin solver. Six L-stable, first- through fourth-order time-integration methods are discussed and exercised on two canonical test cases: the convecting isentropic vortex and the two-dimensional circular cylinder in crossflow. All results are shown on grids composed of P2 (third-order) elements. The isentropic vortex case is used to verify temporal order of accuracy, assess the relative split between dissipative and dispersive errors for each method with various time steps, and quantify the relative computational cost of each method. The results from the two-dimensional circular cylinder in crossflow simulations at various Reynolds numbers are compared to experimental results and accepted numerical results for vortex shedding frequency (Strouhal number), mean drag coefficient, and RMS lift and drag coefficient. The convergence of those parameters with respect to time step size is shown. These results highlight the benefits of high-order (greater than second order) time-integration methods and the need for time-step convergence studies on unsteady simulations.

Janus surface concept for three-dimensional turbulent flows

Three-dimensional numerical simulations of turbulent flow over a partial super-hydrophobic cylinder, hereinafter referred to as the “Janus cylinder”, are performed using large-eddy simulation (LES) with OpenFOAM solver. The slip-wall velocity at the super-hydrophobic surface is evaluated from a third-type (Robin) boundary condition whose coefficient is adjusted based on the available experimental data. Compared to no-slip smooth cylinder, the Janus cylinder has a lower drag coefficient and a lower root-mean-square (rms) lift coefficient, whereas its dominant vortex shedding frequency is higher. The power density distribution of the oscillations, obtained from the Fourier transform of the time-history of the lift coefficient, of the Janus cylinder has a less-sharp and broader distribution compared to the one of the smooth cylinder. No significant difference is observed between the wall shear stress distributions of a Janus cylinder, where super-hydrophobic surface covers only the frontal half of the cylinder, and a totally super-hydrophobic cylinder. This helps the potential manufacturers to reduce the manufacturing costs by partially processing the surface while achieving the highest possible drag reduction.

Numerical simulation of two-dimensional laminar unsteady flow past a right trapezoidal cylinder at low Reynolds number: study of sharpening angle, time step, grid independence and domain size

Numerical simulation of two-dimensional laminar unsteady flow past a right trapezoidal cylinder at low Reynolds number (Re = 100), zero of the flow approaching angle and sharpening angle of the right trapezoidal of 22.5° with a side ratio B/A = 1 are carried out to provide moreapplicable data for engineering design of barred tee in aspect of structural integrity. A finite volume method, non-uniform meshing with second-order implicit time discretization into eight-node quadratic quadrilateral finite elements is employed. An incompressible flow SIMPLEC code with constant fluid properties is used. The convective terms using a third-order QUICK scheme. The numerical simulation result is compared against the published results of flow past a square cylinder. The effect of sharpening angle on the response of the right trapezoidal cylinder is investigated. A special study of the effects of flow on significant factor for time step, grid independence, blockage ratio, domain size, upstream and downstream extents, size domain next to cylinder and size domain extent are performed systematically. The Strouhal number and RMS lift coefficients of fully saturated flow are calculated. The result shown that increasing of sharpening angle, the Strouhal number is negligible changed whilst the RMS lift coefficients significantly increased.

EFFECT OF CORNER MODIFICATION ON TWO-DIMENSIONAL TURBULENT FLOW AROUND A SQUARE CYLINDER WITH INCIDENCE

RNG k- model is used to analyze the aerodynamic performance of an isolated square cylinder with different wind angles, turbulence intensities and corners shapes (sharp, chamfered and rounded). The analysis is made for unsteady two-dimensional turbulent flow. The results are presented in the form of drag coefficient, lift coefficient, RMS lift coefficient and Strouhal number. The present work is compared with previous experiments from published literature and the data gave a qualitative agreement. It is found that drag coefficient, lift coefficient, RMS lift coefficient and Strouhal number are sensitive to angle of incidence, turbulence intensity and corner modification. The average reduction in drag coefficient of square cylinder with modified corners is about 44.5 % for 6.5% turbulence intensity and 41.5 % for 14 % turbulence intensity compared with that of square cylinder with sharp corners. Results indicated that the best fit equation of drag coefficient of sharp corners square cylinder at 45 angle of incidence and 14% turbulence intensity in terms of Reynolds number; ranging from 3.0×104 to 2.825×105, is the second order polynomial equation; Cd = 0.0536×(Re/105)2 - 0.3518×(Re/105) + 2.0128.

Three-dimensional flow around two circular cylinders of different diameters in a close proximity

Flow past two cylinders of different diameters in close proximity is simulated numerically for a constant diameter ratio of 0.45, a gap ratio of 0.0625, and a Reynolds number of 1000 (defined using the diameter of the main cylinder). The effect of the position angle α of the small cylinder relative to the large one on force coefficients and wake flow patterns are studied. Depending on the position angle α of the small cylinder, four wake flow modes are identified: the upstream interference mode for α = 0°, 22.5°, and 45°, the intermittent attached gap flow mode for α = 67.5° and 90°, the attached gap flow mode for α = 112.5° and 135°, and the wake interference mode for α = 157.5° and 180°. The RMS lift coefficients of both cylinders are reduced significantly compared with that of a single cylinder, regardless of the position angle of the small cylinder. Although the variation trends of the mean drag and lift coefficients with the position angle of the small cylinder obtained from the two-dimensional (2D) and three-dimensional (3D) simulations are similar, the 2D simulations overestimate the mean drag coefficient, the RMS drag and lift coefficients compared with those obtained from the 3D simulations.

Numerical simulation with a TVD–FVM method for circular cylinder wake control by a fairing

A water drop-shaped fairing is applied to control the wake behind a circular cylinder and to suppress the formation of Karman vortex street in this paper. The results are evaluated using high resolution CFD technique. A finite-volume total variation diminishing (TVD) approach based upon the recently proposed elemental velocity vector transformation (EVVT) method, which aims at solving the incompressible turbulent flow for irregular boundary conditions with renormalization group (RNG) turbulence model, is used to simulate the flow field around circular cylinder systems. The calculations are carried out with cylinder systems with and without fairings, while the fairings have different top shape angles within the range of 30°~90°. The Reynolds number ranges from 1000 to 50000. It is shown that the simulation results of present numerical method reaches good agreement with the available experimental and numerical simulation data of typical circular cylinder flow and a fixed fairing cylinder system flow. Compared with bare cylinder, the faired bluff structures can obviously reduce the lift and drag forces and alter the vortex shedding frequency. Overall, the mean drag coefficient can be reduced up to about (10–31)% and the RMS lift coefficient can be reduced up to (30–99)% for all faired systems at given Reynolds numbers. The influence of Reynolds number and attack angles on the flow field characters of bare cylinder and faired cylinders is also discussed. The faired structures with shape angles within 30°~45°under zero-attack-angle-inflow case are considered as the optimal structures, with which the mean drag coefficient and the RMS lift coefficient can be reduced up to (26–31)% and (98–99)%, respectively. Considering the influence of attack angles on lift and drag coefficients reduction, 75° shaped faired structure may be taken as a proper option.

Local scour around two pipelines in tandem in steady current

In this study, local scour around two identical pipelines in a tandem arrangement are investigated numerically. The two-dimensional Reynolds-averaged Navier–Stokes (RANS) equations, together with the conservation equation of the sediment mass are solved to simulate the flow around two pipelines and the evolution of the local scour profile below the pipelines. The gap ratios between the two pipelines (G/D) range from 0.5 to 5 with an interval of 0.5, where G is the gap between the two pipelines and D is the diameter of the pipelines. The focus of the study is to investigate the effects of the gap ratio on the scour depth and scour time scale. It is found that the scour depth below the downstream pipeline is greater than that below the upstream pipeline under both clear water and live bed conditions because of the effect of the vortex shedding from the upstream pipeline. The maximum scour depth below the downstream pipeline occurs at G/D=2.5 under both clear water and live bed conditions, which is about the critical gap ratio beyond which vortex shedding from the upstream pipeline occurs. As the gap ratio exceeds 2.5, the scour depth below the downstream pipeline decreases with increasing gap ratio due to the weakening effect of the vortex shedding from the upstream pipeline on the scour. The scour under the clear water condition is simulated at a velocity 25% lower than the critical velocity for live bed scour. The variations of the scour depths below the two pipelines in the clear water and live bed conditions are found to be similar to each other. Strong positive mean lift coefficient on the downstream pipeline was observed during the scour process, which is believed to have a negative effect on the stability of downstream pipeline. The RMS lift coefficient on the downstream pipeline increases significantly when the vortex shedding from the upstream pipeline occurs.

NUMERICAL SIMULATIONS OF LOW REYNOLDS NUMBER FLOWS PAST ELASTICALLY MOUNTED CYLINDER

The vortex-induced vibration (VIV) phenomenon has drawn the attention of researchers in Engineering for several decades. An example is the riser used for petroleum exploration, in which it is subjected to marine flows that may cause oscillations due to vortex shedding. In this paper, numerical analyses of the phenomena that occur in the interaction among flows at low Reynolds numbers and elastically mounted cylinders are presented. The simulation is carried out by using the numerical model Ifeinco that uses a semi-implicit two-step Taylor-Galerkin method to discretize the Navier-Stokes equations and the arbitrary Lagrangean-Eulerian formulation to follow the cylinder motion. The rigid body motion description is calculated by using the Newmark method. Firstly, the characteristics of the vortex generation process for the fixed cylinder are analyzed. In this case, the Strouhal number, the mean drag and the RMS lift coefficients for Reynolds numbers ranging from 90 to 140 are shown. Afterwards, an analysis of a flexible supported cylinder (with a spring and a damper) in transverse direction subject to flows with Reynolds numbers ranging from 90 to 140 is carried out. The cylinder displacement and the vibration frequencies are studied; the synchronization between the vortex shedding and the vibration frequency (lock-in) is analyzed. Similar results to the experimental ones developed by Anagnostopoulos and Bearman (1992) were obtained in this study.

Partially Averaged Navier–Stokes (PANS) Method for Turbulence Simulations—Flow Past a Square Cylinder

The partially averaged Navier–Stokes (PANS) approach is a bridging closure model intended for any level of resolution between the Reynolds averaged Navier–Stokes (RANS) method and direct numerical simulations. In this paper, the proposed closure model is validated in the flow past a square cylinder. The desired ratio of the modeled-to-resolved scales in the PANS closure is achieved by appropriately specifying two bridging parameters: the ratios of unresolved-to-total kinetic energy (fk) dissipation (fε). PANS calculations of different bridging parameter values are performed and the results are compared with experimental data and large-eddy simulations. The Strouhal number(St), mean/root-mean-square (RMS) drag coefficient (CD), RMS lift coefficient (CL), mean velocity profiles, and various turbulent stresses are investigated. The results gradually improve from the RANS level of accuracy to a close agreement with the experimental results with decreasing value of the bridging parameter fk. Overall, the results indicate that the PANS method clearly satisfies the basic tenets of a bridging model: (i) provides a meaningful turbulence closure at any modeled-to-resolved scale ratio and (ii) yields improved accuracy with increasing resolution (decreasing modeled-to-resolved ratio).

Forced‐convection heat transfer from tandem square cylinders in cross flow at low Reynolds numbers

AbstractThis paper presents the results of a numerical study on the flow characteristics and heat transfer over two equal square cylinders in a tandem arrangement. Spacing between the cylinders is five widths of the cylinder and the Reynolds number ranges from 1 to 200, Pr=0.71. Both steady and unsteady incompressible laminar flow in the 2D regime are performed with a finite volume code based on the SIMPLEC algorithm and non‐staggered grid. A study of the effects of spatial resolution and blockage on the results is provided. In this study, the instantaneous and mean streamlines, vorticity and isotherm patterns for different Reynolds numbers are presented and discussed. In addition, the global quantities such as pressure and viscous drag coefficients, RMS lift and drag coefficients, recirculation length, Strouhal number and Nusselt number are determined and discussed for various Reynolds numbers. Copyright © 2008 John Wiley &amp; Sons, Ltd.

Effects of hydrophobic surfaces on the drag and lift of a circular cylinder

Effects of hydrophobic surfaces on the drag and lift of a circular cylinder at Reynolds numbers of 300 and 3900 are investigated using numerical simulations. A cylinder of which the entire surface is no-slip, a cylinder of which the entire surface is hydrophobic, and cylinders with alternating circumferential bands of slip and no-slip conditions are considered. The width of the alternating bands ranges from 0.5λz to 2λz, where λz is a spanwise characteristic wavelength in the near wake. At Reynolds number 300, the hydrophobic surface consisting of alternating slip and no-slip bands of width λz is found to be most effective in enhancing wake instability, thereby decreasing the base suction, drag, and rms lift coefficients. At Reynolds number 3900, hydrophobic surface treatments are found to delay flow separation, thereby decreasing the drag and rms lift.

Numerical predictions of low Reynolds number flows over two tandem circular cylinders

Flows over two tandem cylinders were analysed using the newly developed collocated unstructured computational fluid dynamics (CUCFD) code, which is capable of handling complex geometries. A Reynolds number of 100, based on cylinder diameter, was used to ensure that the flow remained laminar. The validity of the code was tested through comparisons with benchmark solutions for flow in a lid-friven cavity and flow around a single cylinder. For the tandem cylinder flow, also mesh convergence was demonstrated, to within a couple of percent for the RMS lift coefficient. The mean and fluctuating lift and drag coefficients were recorded for centre-to-centre cylinder spacings between 2 and 10 diameters. A critical cylinder spacing was found between 3.75 and 4 diameters. The fluctuating forces jumped appreciably at the critical spacing. It was found that there exists only one reattachment and one separation point on the downstream cylinder for spacings greater than the critical spacing. The mean and the fluctuating surface pressure distributions were compared as a function of the cylinder spacing. The mean and the fluctuating pressures were significantly different between the upstream and the downstream cylinders. These pressures also differed with the cylinder spacing.

Mathematical model of acrosswind dynamic loads on rectangular tall buildings

By investigating acrosswind forces on rectangular cylinders with various side ratios at normal attack angle in a boundary layer wind tunnel, this paper presents empirical formula of acrosswind force spectra, RMS lift coefficients and Strouhal numbers of rectangular tall buildings, and coherence functions of acrosswind force are also probed. Thus, a complete analytical model of acrosswind dynamic loads on rectangular tall buildings is established. This model is in good agreement with the experimental results obtained by wind tunnel tests; so it is reliable and applicable. A calculation method based on this model can be developed to evaluate wind-induced acrosswind responses of rectangular tall buildings in frequency domain.

Cross-wind excitation of a 2D square prism with vibrating leading edge flaps

This paper presents and discusses the results of wind tunnel measurements of the pressure distributions on the lateral sides of a 2D square prism with vibrating leading edge flaps. The flaps were driven with sinusoidal motion at different frequencies and amplitudes. Differential pressures across the lateral sides of the model were sampled simultaneously to give sets of signals at five different distances from the front surface. RMS lift coefficients and lift spectra were calculated by integrating pressures. It was found that increasing the flapping frequency and amplitude decreased the RMS lift coefficient up to 70%. An optimum mean flap angle existed with specific frequency and amplitude. Frequency domain analysis revealed that increased flapping amplitude disrupted vortex shedding, while increased flapping frequency suppressed pressure fluctuations in a wide frequency band. Co-spectra results showed that the flapping action affected the pressure on the side of the model as if the onset flow was made more turbulent. The results suggest that the vibrating flaps introduce a force fluctuation at the flap operating frequency. It appears as if the fluctuating velocity components introduced by the flapping motion work in a manner similar to small-scale turbulence in turbulent onset flow and change the characteristics of the shear layer. Preliminary tests using one flap gave results which confirmed the presence of completely different flows on the opposing faces.

Spanwise correlations of pressure on a rigid square section cylinder

Pressures are spatially averaged through manifolds in order to obtain local instantaneous forces exerted on the sides of a square cylinder at zero incidence. Local lift, obtained from these manifolds, depends on the correlation of the forces on opposite sides of the cylinder. Measurements show that the local RMS lift co-efficient is about 1.4 in low turbulence, dropping as turbulence is added to the free stream. This is in agreement with earlier measurements. Correlation lengths for pressures measured on the same side of the cylinder are about 5.5 times the cylinder dimension in low turbulence, and they also drop with the addition of free stream turbulence. This observation confirms earlier measurements made by Vickery and others and is in contrast to observations reported by Namiranian and Gartshore using other methods. Short-term average correlations are defined and used to show that there is a tendency for the pressure fluctuations at positions separated along the span to remain more nearly in phase and 180° out of phase than would be expected, particularly at large separation distances. Turbulence eliminates this tendency. Some practical implications of this observation are discussed, through estimations of the number of cycles for which the short-term average correlation remains high, on average.

Hydrodynamic Forces on Large Cylinders in Oscillatory Flow

The hydrodynamic forces on a cylinder exposed to oscillatory flow have been determined at Reynolds numbers (Re) in the range 2.5×105 to 1.0×106 (supercritical and transcritical regimes) and Keulegan‐Carpter (KC) numbers in the interval from 1 to 16. One smooth and two rough cylinders were tested. Inline force coefficients and rms lift coefficients are given as a function of KC, Re, and surface roughness. Time series of both force components are shown, and different flow regimes are identified. These force traces are linked to characteristic vortex shedding modes in different KC‐intervals. Both force components are found to vary considerably in the KC‐range under investigation, with the transverse force sometimes being as large in magnitude as the in‐line force.

Aerodynamic forces on structures of circular cross-section. Part 1. Model-scale data obtained under two-dimensional conditions in low-turbulence streams

Data gathered from a number of experiments concerned with the flow around circular cylinders are reviewed. This paper is confined to the consideration of data from laboratory experiments conducted under two-dimensional conditions and in low turbulence streams. Particular attention is paid to the influence of the roughness of the surface of the cylinder on the magnitude of the mean drag coefficient, the Strouhal number and the RMS lift coefficient. An attempt is made to reduce the different roughness types, used to artificially roughen the cylinders, to a common measure of roughness. For each of the aerodynamic coefficients mentioned above quantitative descriptions of their behaviour, at postcritical Reynolds numbers, as functions of roughness are suggested. The work presented here is part of a wider study concerning the across-wind vibrations of structures such as chimneys and towers. There are two companion papers, the first of which considers the influence of turbulence and three-dimensional effects on the aerodynamic coefficients, and the second considers coefficients measured at full scale.