Pulsations, acoustical

Pulsation can be problematic and difficult to predict. Pulsations are also dependent on acoustic resonance charac teristics. 

When a pulsation frequency coincides with a mechanical or acoustic resonance, severe vibration can result. A common cause for pulsation is the presence of flow control valves or pressure regulators. These often operate with high pressure drops (i.e., high flow velocities), which can result in the generation of severe pulsation. Flashing and cavitation can also contribute. 

The pulsation control elements can have several forms, such as plain volume bottles, volume bottles with baffles, bottles and orifices, and proprietary acoustical filters. See Figure 3-26 for an example of a compressor with a set of attached volume bottles. Regardless of which device or element is selected, a pressure loss evaluation must be made before the selection is finalized because each of these devices causes a pressure drop. 

Screw compressors of the dry type generate high frequency pulsations that move into the system piping and can cause acoustic vibration problems. These would be similar to the type of problems experienced in reciprocating compressor applications, except that the frequency is higher. While volume bottles will work with the reciprocator, the dry type screw compressor would require a manufacturer-supplied proprietary silencer that should take care of the problem rather nicely. 

Reciprocating compressor pulsations were covered in Chapter 3, but neeti to be mentioned with the discussions on reliability. Problems with reciprocating compressor pulsations and the potential for acoustic and mechanical resonances are very similar to those experienced with helical-lobe compressors. The significant difference is the frequencies are much lower and the number of discrete frequencies per compressor aie much less. However, piping vibrations can occur and there is always a... 

Each cylinder should have suction and discharge pulsation bottles to dampen the acoustical vibrations caused by the reciprocating flow,... 

Because of the reciprocating action of the piston, care must be exer-ci.sed to size the piping to minimize acoustical pulsations and mechanical vibrations. As a rule of thumb, suction and discharge lines should be sized for a maximum actual velocity of 30 ft/.sec (1,800 ft/min) to 42 ft/sec (2,500 ft/min). Volume 1 contains the necessary formulas for determining pressure drop and velocity in gas piping. 

A pulsation dampener is an acoustic filter designed for minimum transmission of all the frequencies generated as... 

It is important to note that all designers do not agree that the problem of pulsation is acoustical in nature, and hence the approach to solving the problems will necessarily be different. 

For the application and design of a reduced pulsation-vibration system, the acoustic computer technique developed by Southwest Research Institute for the Gas Machinery Research Council in cooperation with the Pipeline and Compressor Research Council is considered the most... 

Example 13-3. Sizing a Pulsation Dampener Using Acoustic Method... 

Abstract Acoustic cavitation is the formation and collapse of bubbles in liquid irradiated by intense ultrasound. The speed of the bubble collapse sometimes reaches the sound velocity in the liquid. Accordingly, the bubble collapse becomes a quasi-adiabatic process. The temperature and pressure inside a bubble increase to thousands of Kelvin and thousands of bars, respectively. As a result, water vapor and oxygen, if present, are dissociated inside a bubble and oxidants such as OH, O, and H2O2 are produced, which is called sonochemical reactions. The pulsation of active bubbles is intrinsically nonlinear. In the present review, fundamentals of acoustic cavitation, sonochemistry, and acoustic fields in sonochemical reactors have been discussed. 

In Fig. 1.1, the parameter space for transient and stable cavitation bubbles is shown in R0 (ambient bubble radius) - pa (acoustic amplitude) plane [15]. The ambient bubble radius is defined as the bubble radius when an acoustic wave (ultrasound) is absent. The acoustic amplitude is defined as the pressure amplitude of an acoustic wave (ultrasound). Here, transient and stable cavitation bubbles are defined by their shape stability. This is the result of numerical simulations of bubble pulsations. Above the thickest line, bubbles are those of transient cavitation. Below the thickest line, bubbles are those of stable cavitation. Near the left upper side, there is a region for bubbles of high-energy stable cavitation designated by Stable (strong nf0) . In the brackets, the type of acoustic cavitation noise is indicated. The acoustic cavitation noise is defined as acoustic emissions from... 

Fig. 1.1 The regions for transient cavitation bubbles and stable cavitation bubbles when they are defined by the shape stability of bubbles in the parameter space of ambient bubble radius (R0) and the acoustic amplitude (p ). The ultrasonic frequency is 515 kHz. The thickest line is the border between the region for stable cavitation bubbles and that for transient ones. The type of bubble pulsation has been indicated by the frequency spectrum of acoustic cavitation noise such as nf0 (periodic pulsation with the acoustic period), nfo/2 (doubled acoustic period), nf0/4 (quadrupled acoustic period), and chaotic (non-periodic pulsation). Any transient cavitation bubbles result in the broad-band noise due to the temporal fluctuation in the number of bubbles. Reprinted from Ultrasonics Sonochemistry, vol. 17, K.Yasui, T.Tuziuti, J. Lee, T.Kozuka, A.Towata, and Y. Iida, Numerical simulations of acoustic cavitation noise with the temporal fluctuation in the number of bubbles, pp. 460-472, Copyright (2010), with permission from Elsevier...

In Fig. 1.4a, an example of the radius-time curve for a stably pulsating bubble calculated by the modified Keller equation is shown for one acoustic cycle [43]. After the bubble expansion during the rarefaction phase of ultrasound, a bubble strongly collapses, which is the inertial or Rayleigh collapse. After the collapse, there is a bouncing radial motion of a bubble. In Fig. 1.4b, the calculated flux of OH... 

In some literature, there is a description that a bubble with linear resonance radius is active in sonoluminescence and sonochemical reactions. However, as already noted, bubble pulsation is intrinsically nonlinear for active bubbles. Thus, the concept of the linear resonance is not applicable to active bubbles (That is only applicable to a linearly pulsating bubble under very weak ultrasound such as 0.1 bar in pressure amplitude). Furthermore, a bubble with the linear resonance radius can be inactive in sonoluminescence and sonochemical reactions [39]. In Fig. 1.8, the calculated expansion ratio (/ max / Rq, where f max is the maximum radius and R0 is the ambient radius of a bubble) is shown as a function of the ambient radius (Ro) for various acoustic amplitudes at 300 kHz [39]. It is seen that the ambient radius for the peak in the expansion ratio decreases as the acoustic pressure amplitude increases. While the linear resonance radius is 11 pm at 300 kHz, the ambient radius for the peak at 3 bar in pressure amplitude is about 0.4 pm. Even at the pressure amplitude of 0.5 bar, it is about 5 pm, which is much smaller than the linear resonance radius. 

In a multibubble field, every pulsating bubble radiates secondary acoustic wave called acoustic cavitation noise. The pulsation of a bubble is driven by both the primary ultrasound and the acoustic cavitation noise. The influence of the latter on the bubble pulsation is called bubble-bubble interaction [89, 90]. Generally speaking, the bubble-bubble interaction suppresses the bubble expansion as shown in Fig. 1.16 [38, 89-91]. Further studies are required on this topic. 

The beholder s perception of the slow pulsation is intensified by an interference effect as well as by acoustic effects that can only be heard when standing in certain positions with respect to the object. 

It has been pointed out by numerical experiments that pulsating bubbles subject to acoustic waves can exhibit chaotic behavior [51]. A second-order model for the pulsating bubbles which is governed by slow variations in amplitude was analyzed in [51]. The ehect of parameters such as amplitude and frequency of the external wave was found to induce chaotic behavior. 

Pulsation can be problematic ancfdifficult to predict. Pulsations are also dependent on acoustic resonance characteristics. For reciprocating equipment, such as reciprocating compressors and pumps, in some cases, an analog (digital) study needs to be performed to identify the deficiency in the piping and pipe support systems as well as to evaluate the performance ofthe machine during operation. The study will also provide recommendations on how to improve the machine and piping system s performance. 

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