Bubbles pressure recovery

The most frequently encountered flashing problems are in control valves. Downstream from the control valve a point of lowest pressure is reached, followed by pressure recovery. A liquid will flash if the low pressure point is below its vapor pressure. Subsequent pressure recovery can collapse the vapor bubbles or cavities, causing noise, vibration, and physical damage. 

One of the simplest approaches to quantify the pressure field downstream of the constriction used to generate cavitation is to assume linear pressure recovery profile. Yan et al. [8] have used similar approach also considering a single bubble to be existing independent of the other bubbles. Such an approach may be adequate when the intensity of turbulence is quite low i.e. for a venturi type constriction or any other constriction with a smooth variation in the cross-sectional flow area. The pressure recovery from the point at which cavitation starts to any downstream pipe position can be approximated by a linear expression with respect to the distance downstream of the constriction. In such a case, the local pressure at any downstream position can be estimated as ... 

Recovery is a measure of the degree of pressure recovery at the valve outlet from the low pressure at the vena contracts. When flashing occurs at the vena contracts and the pressure recovery is high, the bubbles collapse with resulting cavitation and noise. The more streamlined the valve, the more complete the pressure recovery thus, from this point of view streamlining seems to be an undesirable quality. A table of recovery factors of a number of valve types is given by Chaffin (1980) such data usually are provided by manufacturers. 

Cavitation and Flashing From the discussion of pressure recovery it was seen that the pressure at the vena contracta can be much lower than the downstream pressure. If the pressure on a liquid falls below its vapor pressure pv, the liquid will vaporize. Due to the effect of surface tension, this vapor phase will first appear as bubbles. These bubbles are carried downstream with the flow, where they collapse if the pressure recovers to a value above pv. This pressure-driven process of vapor bubble formation and collapse is known as cavitation. 

The solution consists of four major steps (1) calculation of orifice and pipe velocities and pressure recovery time, (2) modeling of the turbulence downstream of the orifice, (3) solution of the bubble dynamic equation to obtain the important parameters of the reactor as functions of time, and (4) use of the results obtained in step 3 to design the... 

Then this instantaneous pressure, which incorporates the eflect of fluctuations due to turbulence, is used in place of in the bubble dynamics equation given by Equation 22.6, assuming that linear pressure recovery does not collapse the cavity (Moholkar and Pandit, 1999). 

The bubble-dynamics equations are very similar to acoustic cavitation the only difference being the fact that the surrounding fluctuating pressure field is driven by hydrodynamic conditions existing downstream of the constriction, whereas in the case of acoustic cavitation, it is dependent on the frequency and intensity of the ultrasonic irradiation (sinusoidal variation). There are two approaches used for the estimation of the local pressure at any location downstream of the constriction (the typical pressure recovery profiles are shown in Fig. 8.2.6). 

Moholkar and Pandit (2001b) have also extended the nonlinear continuum mixture model to orifice-type reactors. Comparison of the bubble-dynamics profiles indicated that in the case of a venturi tube, a stable oscillatory radial bubble motion is obtained due to a linear pressure recovery (with low turbulence) gradient, whereas due to an additional oscillating pressure gradient due to turbulent velocity fluctuation, the radial bubble motion in the case of an orifice flow results in a combination of both stable and oscillatory type. Thus, the intensity of cavitation... 

Nishimura T (2004) Pressure recovery in magma due to bubble growth. Geophys Res Lett 31(12) L12613. doi 10.1029/2004gl019810... 

Mixed plastics waste appears to be well suited for use in energy recovery, either as a co-eombustion fuel in a power plant designed for solid fuels, or as the sole fuel in speeially designed plants. This paper reports test results on the co-combustion of mixed household plasties with eoal. The tests were performed in a bubbling fluidised bed low-pressure steam boiler. The results show that both inorganic and organic total specific emissions were lower for mixed household plasties than for coal. Tabulated data are presented. 3 refs. 

Monolithic columns, formed from the co-polymerization of divinylbenzene and vinylbenzyl chloride or styrene, were observed to be resistant to bubble formation.11 Application of pressure in electrochromatography, discussed below, also reduces bubble formation. A massively parallel detector capable of scanning up to 1000 capillaries using planar confocal fluorescence has been used for DNA sequencing.1213 Recovery of fluorescence following pho-tobleaching has been used to measure DNA mobility in agarose gel.14... 

Equations, determine sequences of simple and complex columns that minimize the overall vapor load. The recoveries will be assumed to be 100%. Assume the actual to minimum reflux ratio to be 1.1 and all the columns, with the exception of thermal coupling and prefractionator links, are fed with saturated liquid. Neglect pressure drop through columns. Relative volatilities can be calculated from the Peng-Robinson Equation of State with interaction parameters set to zero. Pressures are allowed to vary through the sequence with relative volatilities recalculated on the basis of the feed composition for each column. Pressures of each column are allowed to vary to a minimum such that the bubble point of the overhead product is 10°C above the cooling water return temperature of 35°C (i.e. 45°C) or a minimum of atmospheric pressure. 

---