Chemical Engineering Use of Catalyzed Sulfite Oxidation Kinetics for the Determination of Mass Transfer Characteristics of Gas-Liquid Contactors

Transient and statistical measurement techniques for two-phase flows: A critical review

Separated two-phase flow model: application to critical two-phase flow

Mass transfer in multiphase agitated contactors

Holography provides a method of storing the information (size and relative position) of a dynamic three-dimensional distribution of particles so that a stationary image can be produced for detailed study. The depth of field is considerably better than normal image formation. The major technique involves forming an in-line Fraunhofer hologram; this hologram is the interference pattern formed between the far field diffraction pattern of the particles and an in-line background. Off-axis holography can also be used. The basic principles of these methods are described, and practical limitations and advantages discussed. Application of the methods to fog, mist, sprays, rocket engine studies, two phase flow, bubble chamber photography, electron beam holography, etc. are reviewed.

https://iopscience.iop.org/article/10.1088/0022-3735/7/10/001/pdf

Holographic particle sizing techniques

A technique employing the impulse plate principle was developed whereby the ratio of the average vapor-to-liquid velocities (slip ratio) for flowing two-phase mixtures could be measured accurately at high vapor volume fractions. Data were collected for steam-water mixtures flowing adiabatically in a horizontal ½-in. tube. Flow conditions were in the spray annular and dispersed flow regimes and covered a pressure range of 30 to 80 lb.f/sq.in.abs., flow rates of 200 to 800 lb.m/(sec.)(sq.ft.), and steam qualities of 0.02 to 0.8. The experimental slip ratios, ranging between 1 and 3.5, decreased with increasing quality and pressure and increased with increasing mass velocity and pressure gradient.

A theoretical analysis in which an idealized dispersed flow model was used indicated that the observed average slip ratios were caused largely by local slip between vapor and entrained droplets and that high local slip ratios may be attained near critical flow rates due to the simultaneously occurring steep pressure gradients.

The total pressure gradients, computed by adding the Martinelli-Nelson frictional pressure drop prediction to the acceleration pressure gradients calculated by the use of an empirical correlation of the slip ratio data, deviated from the experimental values by an average of only 14%.

A study of slip ratios for the flow of steam‐water mixtures at high void fractions

Critical flow of two-phase steam-water mixtures in annuli was studied, with a cylindrical test section 0.574 in. in diameter with an axially centered rod, 0.187 or 0.375 in. OD, as a pressure probe. Pressure taps on the wall and the center rod permitted an accurate determination of the pressure profile over the entire length of the section, and, in cases where a movable probe was used, a short distance into the downstream exhaust chamber. Results were correlated by plotting the ratio of the observed critical mass velocity to the theoretical critical mass velocity for homogeneous flow as a function of quality. Exit pressures were found to be lower than most values previously reported. The ratio G/sub o//G/sub TH/ was found to be independent of the probe diameter, the manner of upstream steam-water mixing, and, for test sections greater than 9 in. in length, the test section length. Since probe diameter had no observable effect on G/sub o//G/sub TH/, the correlation may be applicable to full bore pipes near 1/2 in. in diameter. In the range of qualities from 2 to 15% the critical G/sub o//G/sub TH/ ratio was depressed with increasing exit (throat) pressure, but at other qualities no pressuremore » dependency was noted. The effect of changing the downstream exhaust chamber pressure was found to influence the exit pressure but to have little effect on the observed critical mass velocity. Addition of surface active agents to the steam-water mixture did not affect the mass velocity but did result in increased exit pressure. (auth)« less

Two‐phase critical flow of steam‐water mixtures

A unified theory of one-dimensional, adiabatic, separated, two-phase flow is presented. To describe the flow adequately, four mixture specific volumes are defined. They are based on area, momentum, kinetic energy, and velocity averages. Increasing relative velocity between the phases initially lowers all mixture specific volumes except the velocity average. The momentum average specific volume minimizes when the slip ratio equals (Vg/Vf)1/2, while the kinetic energy average specific volume reaches its minimum value at a slip ratio of (Vg/Vf)1/3. Area average specific value does not minimize with slip ratio.

Because a higher slip ratio would decrease the entropy of a closed system, (Vg/Vf)1/3 is the maximum slip ratio attainable in two-phase critical flow. Based on the maximum slip ratio and isentropic flow, a new critical flow model was developed and compared with the steam-water critical flow data of four recent investigations. While the predicted flow rates followed well the pressure behavior of the experimental data, they were too low at high qualities and too high at low qualities. The average percentage difference between experimental and predicted critical flow rates was −8.5% (three hundred and seventy-six data points).

Differences in the approach to critical flow between a gas and a vapor-liquid stream appear to be caused by the latter's increased frictional and gravitational pressure drops and relative velocity effects.

Critical flow of liquid‐vapor mixtures

Holographic techniques employing a pulse ruby laser were used to measure the size and velocity of drops for air-water two-phase critical flow at quality levels above 0.95. The use of a large numerical aperture in the holographic recording system permitted diffraction limited resolution of the droplets. The measured slip ratio a long withthe observation that a very significant portion of the liquid phase was concentrated near the boundary layer at the exit plane indicates that a separated flow model describing two-phase critical flow would represent the actual conditions to a better degree than the other models.

Determination of slip ratios in air‐water two‐phase critical flow at high quality levels utilizing holographic techniques

Liquid phase mass transfer coefficients were determined for streams of bubbles of pure oxygen, 10% carbon dioxide in air, and 10% chlorine in air all rising in water. The results were compared with coefficients predicted by Higbie's equation for unsteady state diffusion into transient films. The observed coefficients for oxygen and carbon dioxide were slightly higher than predicted. The experimental absorption coefficients based on the free chlorine concentrations were in good agreement with the predictions assuming simultaneous irreversible reaction with the transient water film and a pseudo first-order reaction rate constant of 13.7 sec.−1.

R. W. Moulton

Papers

A study of slip ratios for the flow of steam‐water mixtures at high void fractions

Two‐phase critical flow of steam‐water mixtures

Critical flow of liquid‐vapor mixtures

Determination of slip ratios in air‐water two‐phase critical flow at high quality levels utilizing holographic techniques

Unsteady state mass transfer from gas bubbles—liquid phase resistance