Vibration in tubes

ESDU 87019 (1987) Flow induced vibration in tube bundles with particular reference to shell and tube heat... 

It explains qualitatively many observations of singing and vibrating flames (and vibrations in tubes containing heated elements as well), described beautifully by Tyndall [53] and dating back at least to an observation made by Dr. B. Higgins in 1777. Of course, the amplification at a burning propellant surface is considerably more complex than the phenomena described by equation (51), since molecular transport processes are involved in an essential way for example (as was seen for the steady-state combustion in Chapter 7). However, the pistonlike mechanism implied by equation (51) when the heat release is localized and the result is expressed in terms of an acoustic admittance [as in equation (29)] is tied closely to the amplification by propellant combustion. 

Pressure Fluctuation Turbulent pressure fluctuations which develop in the wake of a cylinder or are carried to the cylinder from upstream may provide a potential mechanism for tube vibration. The tubes respond to the portion of the energy spectrum that is close to their natural frequency. 

Fig. 5.9a-i Air-water two-phase flow patterns in a 100 pm i.d. clean quartz tube treated with ultrasonic vibration in distilled water, in ethanol and in dilute hydrochloride acid solution. Reprinted from Serizawa et al. (2002) with permission... 

See also, the Engineering Science Data Unit Design Guide ESDU 87019, which gives a clear explanation of mechanisms causing tube vibration in shell and tube heat exchangers, and their prediction and prevention. 

Careful study of various fluids in tubes of different sizes has indicated that laminar flow in a tube persists up to a point where the value of the Reynolds number (NRt = DVp/n) is about 2000, and turbulent flow occurs when NRe is greater than about 4000, with a transition region in between. Actually, unstable flow (turbulence) occurs when disturbances to the flow are amplified, whereas laminar flow occurs when these disturbances are damped out. Because turbulent flow cannot occur unless there are disturbances, studies have been conducted on systems in which extreme care has been taken to eliminate any disturbances due to irregularities in the boundary surfaces, sudden changes in direction, vibrations, etc. Under these conditions, it has been possible to sustain laminar flow in a tube to a Reynolds number of the order of 100,000 or more. However, under all but the most unusual conditions there are sufficient natural disturbances in all practical systems that turbulence begins in a pipe at a Reynolds number of about 2000. 

The pressure drop for the produced carrier or catalyst is measured in the setup shown in Fig. 10. An adjustable flow rate of 300-700 Nm3/h ambient air is supplied by a blower and passed downwards through a bed of catalyst in a long tube. The diameter of the bed is 0.39 m, which is well above the minimum of 10 pellet diameters required for satisfactory reproduction of the void fraction observed in a large fixed bed. The catalyst is poured into the tube from the top and the bed may subsequently be settled by applying a reproducible tapping or vibration to the tube. Since the latter reduces the void and increases the pressure drop, it is important that the catalysts are loaded and vibrated in the same way in order to get comparable results. The pressure drop without catalyst should be checked in order not to introduce errors from the support grid or measuring taps. 

One of the consequences of this is that improvements in the cold drawing of metal tubing can be achieved when the die to be used is subjected to radial ultrasonic vibrations. There are several advantages obtained from drawing round products through a die ultrasonically vibrating in a radial mode, these include ... 

Dunkle also stated that Fay (Ref 12), as quoted from Nicholls (Ref 13), correlated the phenomenon of spin with the natural vibration of the gas particles behind the detonation front. Using the linearized theory of sound as an approximation, Fay developed an equation for spin frequency. For transverse vibrations in a rectangular tube ... 

Vibrations in fired equipment and afterburn. Balanced-draft or induced-draft furnaces and boilers are intended to be operated with a small negative pressure (ca. -0.1 in H20), just below the first row of convective tubes, i.e., just below the shock tubes. If we operate such a piece of equipment with a severe shortage of air in the firebox and massive air... 

Experimental methods presented in the literature may prove of value in combustion studies of both solid and liquid suspensions. Such suspensions include the common liquid spray. Uniform droplets can be produced by aerosol generators, spinning disks, vibrating capillary tubes, and other techniques. Mechanical, physicochemical, optical, and electrical means are available for determination of droplet size and distribution. The size distribution, aggregation, and electrical properties of suspended particles are discussed as well as their flow and metering characteristics. The study of continuous fuel sprays includes both analytical and experimental procedures. Rayleigh s work on liquid jet breakup is reviewed and its subsequent verification and limitations are shown. 

Light vibrating in only one plane passes through the polarimeter tube to the analyser N, which can be rotated about the main axis. The eyepiece at E consists of a system of lenses for focussing. 

When, however, the diameter is increased above 10 cm., the speed of the flames is affected by the coming into play of another factor, namely, convection. This is noticeable with the fastest moving flames in tubes 10 cm. m diameter, the visible effect being a turbulence of the flame front. This is essentially a swirling motion in a direction nearly normal to the direction of translation of the flame front, which, as in tubes of smaller diameter, progresses at a uniform speed for about 150 cm. before backward and forward vibrations are set up. This swirling motion appears ab initio, and is due to rapid movement of the hot gases from below upwards by convection. In tubes of comparatively small diameter (5 to 9 cm.) this rapid movement is suppressed. 

In transitional flow, the flow switches between laminar and turbulent randomly (Fig. 8-5). It should be kept in mind that laminar flow can be maintained at much higher Reynolds numbers in very smooth pipes by avoiding flow disturbances and tube vibrations. In such carefully controlled experiments, laminar flow has been maintained at Reynolds numbers of up to 100,000. 

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