Velocity pulsation

Figure 3.39 Typical vertical distributions over the smooth surface flow (A) mean velocity and pulsation intensity (B) energy spectra of velocity pulsations in logarithmic coordinates on various elevations (1 - z= 2 mm, 2-20, 3-40, 4-60, 5-70, 6-80, 7-90, 8-100, 9-110, 10-130, 110-150 and 12-200 mm).

The instantaneous pressure and velocity distributions along the resonance tube are monitored by piezoelectric transducers and hot-wire thermal anemometer that are connected to the oscilloscope and photo film recorder. These make possible the tuning of the generator to the acoustic resonance by varying the rotational speed of the crankshaft. Also, there is a provision to attach resonance tubes of various lengths and diameters to obtain required amplitudes of pressure and velocity pulsations. 

Unlike pressure, the profile of the velocity pulsation remains practically unchanged along the resonant tube and distortion of the sinusoidal velocity pulsation occurs only at the tube outlet. As shown in Figure 10.3, the amplitude of velocity pulsation decreases sharply with the distance of wave propagation in open air. To take full advantage of the momentum of shock waves, liquid to be dispersed should be fed close to the outlet from the resonant tube, in this case up to about 20 cm. Also, the strongest impact of shock wave due to air velocity might be expected over a distance up to 1 m from the resonance tube. 

The maximum amplitude of the velocity pulsation appears at n = 1 (Figure 10.4). It is quite reasonable to assume that the amplitude of air pulsation at the tube outlet is proportional to the amplitude of the velocity of piston movement... 

More efficient methods for removing adherent dust include the following intermittent blowback at rather high air velocities (pulsating, impulse, etc) with simultaneous breakup of the dust layer mechanical shaking (impact, vibration, pulse, etc.) the use of sonic and ultrasonic vibration filter washing. 

Flow which fluctuates with time, such as pulsating flow in arteries, is more difficult to experimentally quantify than steady-state motion because phase encoding of spatial coordinate(s) and/or velocity requires the acquisition of a series of transients. Then a different velocity is detected in each transient. Hence the phase-twist caused by the motion in the presence of magnetic field gradients varies from transient to transient. However if the motion is periodic, e.g., v(r,t)=VQsin (n t +( )q] with a spatially varying amplitude Vq=Vq(/-), a pulsation frequency co =co (r) and an arbitrary phase ( )q, the phase modulation of the acquired data set is described as follows ... 

The effect of pulsating flow on pitot-tube accuracy is treated by Ower et al., op. cit., pp. 310-312. For sinusoidal velocity fluctuations, the ratio of indicated velocity to actual mean velocity is given by the factor /l + AV2, where X is the velocity excursion as a fraction of the mean velocity. Thus, the indicated velocity would be about 6 percent high for velocity fluctuations of 50 percent, and pulsations greater than 20 percent should be damped to avoid errors greater than 1 percent. Tne error increases as the frequency of flow oscillations approaches the natural frequency of the pitot tube and the density of the measuring fluid approaches the density of the process fluid [see Horlock and Daneshyar, y. Mech. Eng. Sci, 15, 144-152 (1973)]. 

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. 

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. 

The hot-wire anemometer is very accurate even for very low rates of flow. It is one of the most convenient instruments for the measurement of the flow of gases at low velocities accurate readings are obtained for velocities down to about 0.03 m/s. If the ammeter has a high natural frequency, pulsating flows can be measured. Platinum wire is commonly used. 

The assumption of a steady state corresponds to laminar flow of the liquid. This is fulfilled only under certain conditions (limited velocity of the liquid, smooth phase boundary between the flowing liquid and the other phase, etc.). Otherwise, turbulent flow occurs, where the local velocity depends on time, pulsation of the system, etc. Mathematically the turbulent flow problem is a very difficult task and it is often doubtful whether, in specific cases, it is possible to obtain any solution at all. 

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 a hydraulic jig, a mixture of two solids is separated into its components by subjecting an aqueous slurry of the material to a pulsating motion, and allowing the particles to settle for a series of short time intervals such that their terminal falling velocities are not attained. Materials of densities 1800 and 2500 kg/m3 whose particle size ranges from 0.3 mm to 3 mm diameter are to be separated. It may be assumed that the particles are approximately spherical and that Stokes Law is applicable. Calculate approximately the maximum time interval for which the particles may be allowed to settle so that no particle of the less dense material falls a greater distance than any particle of the denser material. The viscosity of water is 1 mN s/m2. 

To elucidate the possible causes of the decrease in suppression potential, the effects of flow residence time and relative pulsating fuel amount were examined. One possible explanation for the above trend is the reduction in flow residence time as the flow rate was increased. At these conditions some of the larger fuel droplets that persisted in the downstream may not have had enough time to react completely if the residence time became very short. When the residence time was estimated by the reference time scale which is the combustor length divided by inlet velocity (Fig. 21.12), the general trend appears to be consistent with the expectation. The scatter in the plot reflects the crudeness of the estimation larger droplets do not follow the carrier flow very well. 

Taylor (T4, T6), in two other articles, used the dispersed plug-flow model for turbulent flow, and Aris s treatment also included this case. Taylor and Aris both conclude that an effective axial-dispersion coefficient Dzf can again be used and that this coefficient is now a function of the well known Fanning friction factor. Tichacek et al. (T8) also considered turbulent flow, and found that Dl was quite sensitive to variations in the velocity profile. Aris further used the method for dispersion in a two-phase system with transfer between phases (All), for dispersion in flow through a tube with stagnant pockets (AlO), and for flow with a pulsating velocity (A12). Hawthorn (H7) considered the temperature effect of viscosity on dispersion coefficients he found that they can be altered by a factor of two in laminar flow, but that there is little effect for fully developed turbulent flow. Elder (E4) has considered open-channel flow and diffusion of discrete particles. Bischoff and Levenspiel (B14) extended Aris s theory to include a linear rate process, and used the results to construct comprehensive correlations of dispersion coefficients. 

In order to obtain very low flow rates without pulsation (e.g. 1 pl/min), pumps based on the principle of high volume motorised syringes are used. The piston, activated by a pneumatic amplifier, moves at a constant linear velocity. These pumps are still in widespread use. 

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