Fluctuating Lift Forces Research Articles

Flow Induced Vibrations in Engineering Systems and the Control of Flow induced Vibrations. Prediction of the Acoustic Instabilities of Tube Arrays in Cross Flow using Numerical Analysis.

The acoustic exciting forces in a duct where a bundle of tubes are in staggered arrangement at a pitch-to-diameter ratio of 2.0 were analyzed using a finite-volume technique which the authors developed on the basis of the GSMAC (Generalized Simplified Marker and Cell) method. Forced oscillating flows with a constant frequency which are perpendicular to a main flow were employed for the analysis of the acoustic vibration field. The fluctuating lift forces on individual tubes in the flow field where the main flow and oscillating flows exist were calculated two-dimensionally. The calculated lift amplitude and the calculated phase difference between the fluctuating lift and the acceleration of forced oscillation, which affects the stability of the acoustic vibration were in good agreement with the values measured in experiment. The finite-volume technique can now be applied to the analysis of acoustic vibrations in the sound field of a duct installed with a bundle of tubes arranged differently.

Simulation of vortex shedding including blockage by the random‐vortex and other methods

AbstractConverged simulations of vortex shedding from a circular cylinder at a Reynolds number of 100 have been computed by the random‐vortex method incorporating the influence of blockage. The results are compared with converged finite‐element and spectral methods and close agreement for Strouhal number is obtained. Forces are, however, in less close agreement, particularly the fluctuating lift force. Strouhal numbers from simulations with zero blockage for Reynolds numbers between 60 and 180 are seen to be in very close agreement with experiments which are said to be effectively two‐dimensional. In this range the Strouhal number changes from 0·135 to 0·191. There are no corresponding experimental measurements for force.

Circular saw aerodynamic noise

The aerodynamically induced noise of an idling circular saw turning at high speed is investigated both experimentally and analytically. The origin of the noise is shown to be fluctuating lift forces acting on the teeth. The sources at the teeth radiate incoherently as baffled dipoles and account for the generated noise. The analysis predicts that the generated sound power will scale on tooth area, and this prediction is confirmed for gullet width to tooth thickness ratios greater than about two, thus establishing tooth area as the second most important scaling parameter following that of saw rotational speed. The fluctuating lift force on a tooth is shown experimentally to increase with the square of the saw rotational speed, while the generated sound power is shown to increase with saw rotational speed to a power slightly greater than five. The analysis shows that the source radiation impedance increases with the frequency of the radiated sound, which in turn increases essentially linearly with saw rotational speed. The fifth power dependence of radiated sound power on saw speed in thus explained as being due to the source location on the teeth at the perimeter of the blade. An instrumented tooth on an artificial saw blade was used to measure the aerodynamically induced local pressure fluctuations. These pressure fluctuations were used to estimate the expected sound at 1·0 m from the saw on the axis of rotation by making use of the analysis. In the analysis it is assumed that the sources at the teeth radiate incoherently to contribute to the observed sound. Fairly good agreement is demonstrated between measurement and prediction.

Excitation by Vortices Shedding Periodically from Two Cylinders in Cruciform Arrangement.

The behavior of the excitation caused by longitudinal vortices shedding from two cruciform circular cylinders with an equal diameter d is investigated using a wind tunnel. When the gap s between two cylinders is less than d/2, longitudinal vortices shed periodically and a fluctuating lift force is exerted on the upstream cylinder. The nondimensional frequency, StM, of the longitudinal vortices is independent of the Reynolds number. The value of StM is 0.06<StM<0.09 when s/d<0.25 (region A) and StM≒0.04 when 0.25<s/d<0.5 (region B). The fluctuating lift force on the upstream cylinder is estimated from the pressure on the cylinder surface using a phase-averaging technique. The result shows that the flow near the crossing of the cylinder is dominated by four trailing vortices in the region A and by two necklace vortices in the region B. These vortices shed an anti-phase on the opposite side of the upstream cylinder, causing an alternative lift force to be exerted on it. The abrupt change of StM at s/d=0.25 is caused by the fact that these two types of vortices interchange their role to excite the upstream cylinder.

Characteristics of Longitudinal Vortices Shedding from Two Circular Cylinders in Cruciform Arrangement.

The behavior of the longitudinal vortices shedding from a cruciform arrangement of two circular cylinders with an equal diameter d is investigated using a wind tunnel. The longitudinal vortices shed periodically near the crossing corner of the cylinders when the gap s between them is less than d/2. The nondimensional shedding frequency, StM, of the longitudinal vortices is independent of the Reynolds number Re when 730<Re<34, 400. The value of StM is : 0.06<StM<0.09 when s/d<0.25 and StMc0.04 when 0.25<s/d<0.5. The fluctuating lift force on the upstream cylinder caused by the longitudinal vortices is estimated from the pressure measured on the cylinder surface. The result correlates well with values obtained from the oscillation amplitude of an elastically supported upstream cylinder. Effects of the oscillation of the upstream cylinder on the longitudinal vortex shedding are also investigated, and a phenomenon similar to the lock-in of the Karman vortex shedding is found in certain ranges of s/d and the free-flow velocity.

Active vibration control of a flexible cylinder subjected to periodically shedding vortices

A mathematical model is developed to simulate the dynamics of a flexible cylinder subjected to vortex-induced excitation. The finite element method is used to describe the dynamic characteristics of the cylinder. The fluctuating lift forces induced on the cylinder are assumed to satisfy a modified Van der Pol equation and are determined by the wake-oscillator approach. The dynamic equations of the cylinder are coupled with the modified independent modal space control (MIMSC) method, which actively suppresses the dominant mode of the vibration. The performance of the active controller of the vortex-induced vibrations is obtained at various flow speeds and control weighting parameter. To verify the mathematical model, the computed results are compared with experimental data obtained in a low-speed wind tunnel over a range of Reynolds numbers between 5500 and 7500. Good agreement is observed between the theory and experiments. It was found that the controller is effective in attenuating the transverse vibrations of the cylinder by approximately 40% for all the flow speeds considered.

Structural safety of an ocean outfall against hurricane damage

Ocean outfall pipelines, made of cast iron with concrete coating, are used to carry secondary-treated effluent which has almost the same density as freshwater. The pipelines, which are laid in trenches backfilled with sand and rock boulders, are often insufficiently protected in the event of a major storm. This paper presents a study on the prediction of the wave/wave-induced hydrodynamic forces and erosion that would result from a hurricane, and evaluates the potential for damage to the structure due to a Category 4 hurricane, i.e. a hurricane (measured on a scale of 1–5) with a wind velocity between 131 and 155 m.p.h. and storm surges of 13–18 ft above normal, which may lead to major beach erosion. The investigation includes liquefaction analysis, evaluation of scour due to wave breaking, vertical and horizontal stability analyses, and recommendations for a concrete flexible revetment scour protection system. Both fully exposed and partially buried pipelines are considered in the stability analysis. A detailed discussion of the main elements of a scour protection system, including the revetment underlayer, cellular units, tendons, and pin anchors is presented, with typical illustrations. Further study is needed to include possible pipeline breakout from the seafloor which results from fluctuating lift forces caused by an induced gap at the pipe-soil interface.

Numerical solution for laminar two-dimensional flow about a fixed and transversely oscillating cylinder in a uniform stream

A finite element solution is presented for laminar 2-dimensional flow past a fixed and transversely oscillating cylinder. The solution of vortex street development behind the cylinder is obtained when the cylinder remains fixed. Then the cylinder which is assumed elastically mounted is allowed to oscillate in the cross-flow direction under the action of the fluctuating lift force. The grid system is translated with the cylinder at each time step and the field variables are interpolated to new grid locations. The computer results predict the lock-in phenomenon which occurs when oscillation frequency is near the natural vortex-shedding frequency. Particular attention was given to flow configuration, by means of streamlines, filament lines, and equi-vorticity lines. The effect of cylinder oscillation on lift and drag forces and separation angles is extracted from the numerical results. Computer results at Reynolds numbers 106 and 115 are in good agreement with experimental measurements conducted by the author.

Wind‐Induced Vibration of Two Flexible Cylindrical Structures

This paper presents a simple mathematical model that can be used to predict the vortex‐excited resonant response of two flexible cylindrical structures in line with the wind direction. A modified van der Pol equation is employed to account for the effect of fluctuating lift forces on the cylinders, and normal mode technique is used for treating the flexibility of the cylinders. The governing equations are nonlinear in nature, and the solutions of these equations are assumed to be in the form of sinusoidal functions. Results obtained are in good agreement with the experimental data.

A laboratory study of the lift forces on a moving solid obstacle in a rotating fluid

Abstract A series of experiments is described in which a novel technique is used to measure directly the lift force on a right cylynder circular moving through a homogeneous rotating fluid. These experiments have been conducted on the large rotating table facility at the Institut de Mecanique de Grenoble, in order to investigate simultaneously flows at high Reynolds number ( Re ), low Rossby ( Ro ), and low Ekman ( Ek ) number. The measurements have shown that within the range of parameters 0.25 Ro −6 Ek −6 ; 1.50 × 10 4 Re 5 , the cylinder experiences a mean lift due to (i) the structural asymmetry between cyclonic and anticyclonic eddies in its wake, and (ii) the Coriolis force on its excess mass. The total mean lift coefficient C ∗ shows no significant dependence upon Ek , but exhibits a linear relationship with Ro −1 . Similarly, the contribution of the mean lift coefficient C p due to the wake asymmetry alone is shown to vary approximately linearly with Ro −1 . In addition to the net mean lift, the cylinder experiences a fluctuating lift force generated by periodic vortex shedding. The amplitude of the fluctuating lift coefficient also increases linearly with increasing values of Ro −1 , though the Strouhal frequency shows no variation with either Ro or Ek . Measured values of the Strouhal number do not differ significantly from values typical of non-rotating flow past circular cylinders.

Fluctuating lift forces and pressure distributions due to vortex shedding in tube banks

Experimental measurements of fluctuating lift forces and surface pressure distributions are presented for staggered and in-line tube banks consisting of four rows, with transverse pitch-to-diameter ratio ( P T/ d) of 2.67 and longitudinal pitch-to-diameter ratio ( P L/ d) of 2.31. A strain gauge system was used to measure the fluctuating force on one instrumented tube located at various positions in the tube banks. A second instrumented tube was equipped with a static pressure tapping and a pressure transducer to provide time average and rms fluctuating surface pressure distributions, respectively. Investigations of the staggered tube bank revealed that the highest levels of fluctuating lift coefficients occurred in the second row. For the in-line geometry, on the other hand, similar levels of fluctuating lift coefficient were found in the second, third, and fourth tube rows. The normal configuration for staggered tube banks as used here is symmetrical. Further tests were undertaken for an asymmetric geometry, revealing a major reduction in the fluctuating lift forces as compared with symmetrical geometry. It is concluded that the use of irregular geometries in staggered tube banks should be further investigated as a practical solution to the reduction of vortex-induced vibrations in tubular heat exchangers.

Experimental Studies on Fluctuating Lift Force on a Single Circular Cylinder at High Reynolds Numbers

Vortex shedding vibration is one of the most important problems to consider in the design of circular cylindrical structures such as the thermowell, the thimble tube for the ICIS and the support columns in nuclear reactors. The objectives of this study are to investigate the vibration response of these structures due to cross flaw aver the range of the high Reynolds numbers, and to propose suggestions to guide future designs of these structures. Experimental studies on the fluctuating lift force which acts on a single circular cylinder for the Reynolds numbers from 3x104 to 3x106 were conducted in a MEI waterchannel test apparatus. The tests were carried out by using two types of models with different stiffness characteristics. One was a stationary model which was used to measure the fluctuating lift force and the Strouhal number. The other was an elastic model which wasused to investigate the vibration response. The results obtained using these two models were a lift coefficient of CL rms and a Strouhal number of st. These results were the same values which have previously been reported by many other investigators. The “locked-in” vibration observed with the elastic model for the critical Reynolds number range was the same phenomena found in the subcritical Reynolds number range.

Vortex excitation of rectangular cylinders with a long side normal to the flow

The vortex excitation of rectangular cylinders having side ratios of 0.2, 0.4 and 0.6, with a long side normal to the flow, in a mode of lateral translation, is investigated experimentally in a wind tunnel using free- and forced-oscillation methods. The range of reduced wind speeds investigated, 3-12, includes the vortex-resonance regime. The forced-oscillation experiment includes measurements of the fluctuating lift force at amplitudes up to 10% of the length of a long side. The experiments were also performed on cylinders with a long fixed splitter plate. The results of the measurements show that vortex excitation of a rectangular cylinder is strongly dependent on the side ratio. It is suggested that the critical change of the mean base pressure of an oscillating rectangular cylinder with increasing side ratio is closely correlated with the vortex-excitation characteristics. The concept of vortex excitation as aeroelastic flutter occurring in a fluid-body coupled system is proposed on the basis of the experimental results. The most essential feature of vortex excitation as a coupled flutter is that the fluid subsystem can be set into resonance by the body motion. A rapid phase-angle change in the lift force through vortex resonance produces a large out-of-phase force component which excites the motion of the body subsystem.

An investigation of the wake structure of a circular cylinder using a computer aided flow visualization. 3rd report. Wake of a cylinder fitted with splitter plates.

Phase-averaged velocity and pressure fields in the wake of a cylinder fitted with splitter plates have been determined using a computer aided flow visualization technique and fluid forces on a cylinder have been evaluated. Some discussions of the mechanism of occurrence of the drag and the fluctuating forces have been shown. Splitter plates have an effect to modify the configurations of shedding vortices as well as one to shift the position of the vortex formation, and long vortices stretched in the flow direction are formed as the formation region shifts downstream. Either the drag or the fluctuating lift forces can be closely correlated with the velocity at a cylinder induced by the shedding vortex and the relations them is mostly linear so far as the induced velocity is small.

Two‐Cylinder Model for Wind Vortex‐Induced Vibration

A simple mathematical model for predicting the vortex‐excited resonant response of two cylinders in line with the wind direction is presented. For the model, a modified van der Pol equation is employed to account for the effect of fluctuating lift force on the cylinder, and this equation is coupled with the equation for the oscillatory motion of the cylinder. The governing equations are nonlinear in nature, and the solutions of these equations are assumed to be in the form of sinusoidal functions. Results obtained are in good agreement with the experimental data.

A lock-in effect in the flow over two cylinders

SummaryMeasurements are presented of the frequency of vortex shedding from two circular cylinders in a staggered arrangement. Seven different cylinders were used in turn as the upstream cylinder and the ratio of the diameter of the upstream cylinder to that of the downstream cylinder ranged from 0·00422 to 0·571. For a constant free-stream velocity changing the upstream cylinder changed the frequency of vortex shedding from the cylinder. It was found that the frequency of vortex shedding from the downstream cylinder N synchronised with that of the upstream cylinder n over a range of the latter frequency. When the frequencies were synchronised the ratio of the frequencies was given by n/N = 2. This behaviour is characteristic of a lock-in process.Lock-in was found at each of the four upstream cylinder positions tried. However, it was only when the upstream cylinder position was such that the upstream cylinder only weakly affected the flow about the downstream cylinder that lock-in was accompanied by a decrease in the base pressure. The time-mean drag force then increased with lock-in, but by a small amount only. On the other hand the fluctuating lift force increased substantially.

Fluctuating pressures and forces acting on downstream circular cylinder in staggered arrangement.

This paper presents the phase-averaged fluctuating pressures and phase-averaged drag and lift forces acting on the downstream cylinder of two staggered circular cylinders. Phase relationship between the fluctuating lift force and the fluctuating pressure on the downstream cylinder is revealed. The phase of the fluctuating lift force acting on the downstream cylinder is trigered by the arrival of vortices shed from the upstream cylinder. The phase difference between the fluctuating lift forces of two cylinders if found to be proportional to the distance between their centres.

Fluctuating pressures and forces acting on downstream cylinder in staggered arrangement.

This paper presents the phase-averaged fluctuating pressures and phase-averaged drag and lift forces acting on the downstream cylinder of two staggered circular cylinders. Phase relationship between the fluctuating lift force and the fluctuating pressure on the downstream cylinder is revealed. The phase of the fluctuating lift force acting on the downstream cylinder is trigered by the arrival of vortices shed from the upstream cylinder. The phase difference between the fluctuating lift forces of two cylinders if found to be proportional to the distance between their centres.

On the aerodynamic noise source in circular saws

The character of the dominant aerodynamic noise source for rotating rigid circular saws is concluded to be represented by a point dipole model. The source strength is directly dependent upon Reynold’s number and saw design. A theoretical model is presented for prediction of the farfield noise. Experimental measurement of the fluctuating lift force on particular tooth models was used to identify the dipole source and a hot wire anemometer, rotating with the saw, measured the tooth wake. The theoretical predictions of dipole noise dependence upon parameter variation are generally consistent with literature noise data.

Lift and moment fluctuations of a cambered aerofoil under nonconvecting streamwise gust

The theory of non-stationary motion around aerofoils has many important applications in the field of aeronautics and turbomachines. The most significant problems are flutter, fluctuating loads experienced by blades of a typical turbomachine which move through a non-uniform field of flow, disturbed by the induced effects of other stationary and moving blade rows. It is important to predict the fluctuating lift force on a blade or aerofoil due to a flow disturbance, because both the blade vibration and noise generation are related to fluctuating lift and moment.