FLOW INDUCED VIBRATIONS

• Vibration and noise problems due to fluid flow occur in many industrial plants.

• This obstructs smooth plant operation. These flow-related phenomena are known as “Flow Induced Vibrations” (FIV).

• The term “Flow-Induced Vibration and Noise” (FIVN) is used when flow-induced noise is present.

• The fluid force acting on an obstacle in flow will vary due to the flow unsteadiness and that the force, in turn, may cause vibration of the obstacle.

• In the case of piping connected to reciprocating fluid machines, it is well known that the oscillating (fluctuating) flow in the piping generates excitation forces causing piping vibration.

• For steady flow conditions, vibration problems are caused by vortex shedding behind obstacles or by other phenomena.

• The flow induced vibration has become increasingly important in recent years because designers using materials to their limits, causing structures to become progressively lighter & more flexible.

• The fluid flow & the structure are interactive systems, and their interaction is dynamic. These systems are coupled by the force exerted on the structure by the fluid.

• The fluid force cause the structure to deform

• As the structure deforms it changes the orientation of the flow and the fluid force may change.

• The dynamic interaction of the structure and the fluid models is described by the nonlinear equations.

FUNDAMENTAL MECHANISMS OF FIV

FIV couples fluid mechanics and vibration engineering

• Self-induced oscillation mechanisms

A system that oscillates under the influence of its own energy source due to its internal physical mechanisms is said to undergo “self-excited vibration”.

• Forced vibration and added mass and damping

Coupled with the self induced oscillation & motion induced by the system itself

The fluid damping can be divided into two categories: damping in still fluid and damping induced by fluid flow. The latter damping depends on many mechanisms.

VIBRATION INDUCED BY CROSS-FLOW

• Cross-flow-induced vibration is the most important problem in various fields, and is known to have caused many failures in various industrial components.

• Fluids are usually classified as either “gas” or “ liquid” When dimensionless numbers, such as Reynolds number, are equal in the two cases, there is no basic difference and both fluid flows may simply be treated as “single-phase flow”

• On the other hand, when gas and liquid exist as a mixture due to evaporation and condensation of steam for instance, a treatment different from single-phase flow is required. This falls in the area of “gas–liquid two-phase flow” analysis.

SINGLE CIRCULAR CYLINDER

• It describes the flow-induced vibration (FIV) problem in the case of a single structure having circular cross-section.

• Examples in this category include components exposed to steady flow, such as thermo wells in pipes, and components exposed to oscillating flow or waves, such as marine pile structures.

• Multi-span slender structures such as cables or riser pipes also fall in this category.

Vibration mechanisms

Divided into two categories

• (i) beam mode bending vibration of the circular cylindrical structures,

• (ii) ovalling vibration of cylindrical shells.

The former is classified into vibration induced by steady flow, for example the problem of cylindrical structures contained in pipes and vibration caused by unsteady (oscillating) flow, as in the case of marine structures. The vibration of circular cylindrical structures in steady flow is further subdivided into four classes.

FORCED VIBRATION BY KARMAN VORTEX SHEDDING

• When flow past a bluff body generates a vortex street in the wake region (this being the well-known Karman vortex street), periodic shedding of these vortices from the surface of the body induces periodic pressure variations on the structure.

• Vibrations in two directions are possible, transverse and parallel to the flow.

• In the transverse direction, the excitation force has a dominant frequency called the Karman vortex shedding frequency.

• In the drag direction the dominant frequency is at twice the Karman vortex shedding frequency.

• The vortex shedding frequency f is expressed in dimensionless form by the Strouhal Number, St.

SYNCHRONIZATION ACCOMPANIED BY ALTERNATING KARMAN OR SYMMETRIC VORTEX STREET

• When the natural frequency of the structure is close to the vortex shedding frequency, the latter frequency synchronizes with the natural frequency of the structure. This phenomenon is termed lock-in.

• Such synchronization can occur both in the transverse and parallel directions to the flow. Moreover, depending on conditions, in-line synchronization in the flow direction accompanied by symmetric vortex shedding may occur at lower flow velocities compared to transverse direction lock-in.

TURBULENCE-INDUCED VIBRATION

• A cylinder is inevitably excited by vortex-induced vibration outside the synchronization region. Not only has this periodic component at a dominant frequency in the excitation force existed, but also components over a wide frequency band.

• If the structural natural frequency is well separated from this dominant (shedding) frequency, it will instead be excited by the wide-band components closest to the natural frequency.

• The resulting response is termed turbulence-induced vibration.

VIBRATION INDUCED BY TIP-VORTICES IN HIGH FLOW VELOCITY REGIME

• Large amplitude vibrations (comparable to synchronization-induced vibrations) may arise at high flow velocities, well beyond the Karman shedding lock-in regime. This phenomenon is caused by vortices generated at the cylinder extremity.

• These tip-vortices are shed at a frequency roughly one-third the Karman shedding frequency. The critical flow velocity for lock-in is therefore three times the critical velocity for Karman shedding.

VIBRATION OF A CIRCULAR CYLINDER IN OSCILLATING FLOW

• When a circular cylinder is subjected to oscillating flow the flow velocity oscillations result in variations of the drag and fluid inertia forces.

• Since vortex shedding from the circular cylinder is also present, excitation transverse to the flow direction also occurs. The result is superposed (in-flow + transverse) bending vibration of the circular cylinder induced by the oscillating flow.

• A feature of the resulting vibration is that the in-line vibration component induced by the flow oscillations is much more dominant.

GALLOPING VIBRATIONS

• If a structure vibrates in a steady flow, the flow in turn oscillates with respect to the moving structure.

• The oscillating component of the flow relative to the structure induces an oscillating aerodynamic force on the structure.

• If the oscillating aerodynamic force tends to diminish the vibrations of the structure, then the structure is said to be aerodynamically stable

• If the oscillating aerodynamic force tends to increase the vibrations of the structure, the structure is said to be aerodynamically unstable

• The flow induced vibrations of bluff bodies are known as stall flutter

• Galloping can arise in lightweight structure, flexible exposed to the flow

• Although galloping vibrations and aircraft flutter arise from similar aero elastic mechanisms, there are important differences between the two.

• In aircraft flutter the aerodynamic forces are often sufficiently large, compared with the weight and inertia of the cross section to produce large shifts in the natural frequency

• In galloping vibrations the aerodynamic force are usually small compared with the massive structure, so shifts in natural frequency are generally very small.

• In addition aerodynamic aircraft flutter is accompanied by the interaction of a torsion mode and a displacement mode, whereas galloping instabilities often affect as a single mode.

• Galloping, also known as Den Hartog instability is the large amplitude, low frequency oscillation of a structure in the direction transverse to the mean wind direction.

• It normally appears in the case of bodies with small stiffness and structural damping, when they are placed in a flow provided the incident velocity is high enough.

• Galloping depends on the slope of the lift coefficient versus angle of attack curve.

• The body is stalled after boundary layer separation, which is a Reynolds number dependent phenomenon.

• Galloping occurs due to the aerodynamic forces that are induced by the transverse motions of the structure.

• These aerodynamic self-excited forces act in the direction of the transverse motion resulting in negative damping, which increases the amplitude of the transverse motion until it reaches a limit cycle.

• Galloping is “Aero elastic” phenomenon in which excitation is produced by the moment of the member. 

• It is a motion in “one degree of freedom”

• And applies to members who can only move in one direction (or rotation).

• It arises when the aerodynamic damping is negative over part of the cycle of oscillation, and so becomes a forcing function. 

• Consider the case of a bluff sharp edged member free to move across a wind stream if the force co-efficient are in wind axes.

• Coefficient of the cross wind force can be written as below as

• Under the action of steady wind, ice-coated transmission lines, cable-suspended bridge decks, and some other flexible structures are often plagued by low-frequency, large-amplitude, across-wind vibration called galloping. 

• At moderate wind speeds, galloping of ice-coated transmission lines of an amplitude greater than 5 m (16 ft) is not unusual.

• Galloping can happen to almost any lightweight, flexible, cylindrical (prismatic) structures, except those of circular cross section, exposed to wind.

• However, some special cross-sectional shapes, such as rectangular sections or D sections, are more prone to galloping than others.

• In the analysis of galloping, it is assumed that the vibration is slow so that a quasi-steady approach is valid for determining the lift and drag from the following steady-state equations

EFFECT OF WIND ON STRUCTURE

• Wind produces three different types of effects on structure: Static, dynamic and aerodynamic. The response of load depends on type of structure.

• When the structure deflects in response to wind load then the dynamic and aerodynamic effects should be analyzed in addition to static effect.

• Sound knowledge of fluid and structural mechanics helps in understanding of details of interaction between wind flow and civil engineering structures or buildings.

• Flexible slender structures and structural elements are subjected to wind induced along and across the direction of wind. When considering the response of a tall building to wind gusts, both along-wind and across-wind responses must be considered.

• These arise from different the former being primarily due to buffeting effects caused by turbulence; the latter being primarily due to alternate-side vortex shedding.

• The cross-wind response may be of particular importance because it is likely to exceed along-wind accelerations if the building is slender about both axes.

WIND INDUCED OSCILLATION

1. Galloping

2. Flutter

3. Ovalling

Galloping

• Galloping is transverse oscillations of some structures due to the development of aerodynamic forces which are in phase with the motion.

• It is characterized by the progressively increasing amplitude of transverse vibration with increase of wind speed.

• Non circular cross section are more susceptible to this type of oscillation

Flutter

• Flutter is unstable oscillatory motion of a structure due to coupling between aerodynamic force and elastic deformation of the structure.

• Perhaps the most common form is oscillatory motion due to combined bending and torsion.

• Long span suspension bridge decks or any member of a structure with large values of d/t (where d is the depth of a structure or structural member parallel to wind stream and t is the least lateral dimension of a member) are prone to low speed flutter.

Ovalling

• Thin walled structures with open ends at one or both ends such as oil storage tanks, and natural draught cooling towers in which the ratio of the diameter of minimum lateral dimension to the wall thickness is of the order of 100 or more, are prone to ovalling oscillations.

• These oscillations are characterized by periodic radial deformation of the hollow structure.

OSCILLATIONS DUE TO DYNAMIC COMPONENT

Gust

• The wind velocity at any location varies considerably with time.

• In addition to a steady wind there are effects of gusts which last for few seconds and yield a more realistic assessment of wind load. In practice the peak gust are likely to be observed over an average time of 3.5 to 15 secs depending on location and size of structure.

• The intensity of gusts is also related to the duration of gusts that affects structures.

• Larger structure will be affected more by gust of larger duration and thus subjected to smaller pressure compared to smaller structure.

• The gust effect factor accounts for additional dynamic amplification of loading in the along-wind direction due to wind turbulence and structure interaction.

• It does not include allowances for across-wind loading effects, vortex shedding, and instability due to galloping or flutter, or dynamic torsional effects.

• Buildings susceptible to these effects should be designed using wind tunnel results.

This factor accounts for the increase in the mean wind loads due to the following factors:

1. Random wind gusts acting for short durations over entire or part of structure.2. Fluctuating pressures induced in the wake of a structure, including vortex shedding

forces.3. Fluctuating forces induced by the motion of a structure.

Vortex Shedding

• When wind acts on a bluff body forces and moments in three mutually perpendicular direction are generated- out of which three are translation and three rotation.

• For civil and structures the force and moment corresponding to the vertical axis (lift and yawing moment) are of little significance. Therefore the flow of wind is considered two-dimensional consisting of along wind response and transverse wind response.

• Along wind response refer to drag forces, and transverse wind is the term used to describe crosswind.

• The crosswind response causing motion in a plane perpendicular to the direction of wind typically dominates over the along-wind response for tall buildings.

• Consider a prismatic building subjected to a smooth wind flow. The originally parallel upwind streamlines are displaced on either side of the building due to boundary layer separation.

• This results in spiral vortices being shed periodically from the sides into the downstream flow of wind creating a low pressure zone due to shedding of eddies called the wake. When the vortices are shed across wind component are generated in the transverse direction.

• At low wind speeds, since the shedding occurs at the same instant on either side of the building, there is no tendency for the building to vibrate in the transverse direction.

• It is therefore subject to along-wind oscillations parallel to the wind direction.

• At higher speeds, the vortices are shed alternately, first from one and then from the other side. When this occurs, there is an force in the along-wind direction as before, but in addition, there is an force in the transverse direction.

• This type of shedding, which gives rise to structural vibrations in the flow direction as well as in the transverse direction, is called vortex shedding.

• The frequency of shedding depends mainly on shape and size of the structure, velocity of flow and to a lesser degree on surface roughness, turbulence of flow.

• For slender structure, the shedding frequency ή shall be determined by the following formula ή =SVd / b

• where

S = Strouhal number, Vd = design wind velocity, and

b = breadth of a structure or structural members in the horizontal plane normal to the wind direction

• Circular Structures - For structures circular in cross-section: S = 0.20 for bVz not greater than 7, and S= 0.25 for bVz, greater than 7.

• Rectangular Structures - For structures of rectangular cross-section: S = 0.15 for all values of bVz Where Vz = Design wind speed

Buffeting

• A downwind structure could oscillate due to vortex shedding of adjacent structure