Local Interfacial Area Concentration Research Articles

Sensitivity study on double-sensor conductivity probe for the measurement of interfacial area concentration in bubbly flow

The sensitivity study on a double-sensor conductivity probe for the measurement of local interfacial area concentration, has been carried out by considering the effects of bubble lateral motions and probe spacing. The measurable value was rigorously related to the local bubble interface velocity in the surface normal direction, and the probability density function of each individual variable was identified with proper coordinate transform. Three theoretical calibration factors were defined to bridge the mean measurable parameter to the interfacial area concentrations carried by the missed bubbles, measured bubbles and their combination. These calibration factors were obtained through numerical method. The results indicate that the total calibration factor is the best choice for practical applications, whereas the other two factors bring in profound understandings of the measuring mechanisms. With the probe spacing varying from about 36–86% of the mean bubble diameter, the total calibration factor is only determined by the bubble velocity fluctuation, almost independent of the probe spacing. The analysis also suggests that the missed bubbles contribute larger interfacial area concentration to the measuring point than that obtained from the measured bubbles. Moreover, for better statistic behaviors, the appropriate sample size was provided using a Monte Carlo approach.

Interfacial Area Concentration and Void Fraction of Two-Phase Flow in Narrow Rectangular Vertical Channels

Adiabatic concurrent vertical two-phase flow of air and water through narrow rectangular channels, gap widths 1 mm and 2 mm, was investigated. This study involved the observation of flow using a charge coupled device (CCD) camera. These images were then digitized and examined by applying an image processing technique to determine local average void fraction and local average interfacial area concentration. The void fraction data were then plotted using a drift flux plot to determine the distribution parameter and vapor drift velocity for each separate flow regime.

Local two-phase flow measurements using sensor techniques

Radial profiles of various local parameters in bubbly two-phase flow were obtained. Measurements of the local void fraction, the local interfacial area concentration, the bubble interfacial velocity and Sauter mean diameter were made using the double sensor probe method. At the same locations, local liquid velocity and turbulence intensity measurements were made using a hotfilm anemometer. Data was taken at three different axial locations ( L/ D=2, L/ D=32 and L/ D=62) along a 3.24 m test section with an inner diameter of 0.0508 m. In comparison to previous data sets, the following data is more complete in the sense that both interfacial area measurements are combined with one of the local driving forces for interfacial transfer, namely the liquid turbulent diffusion. There have been few, if any, studies done combining local liquid turbulence and the local interfacial area concentration. The data taken will eventually be applied to the closure relations required by the one-dimensional, time-averaged interfacial area transport equation.

Development of local two-phase flow parameters for vertical bubbly flow in a pipe with sudden expansion

Experimental data are presented for vertical air-water bubbly flow obtained by fiber-optic sensors in a pipe with sudden expansion (40 mm to 90 mm). The local void fraction, local bubble velocity, local bubble frequency, bubble chord length, bubble size, and local interfacial area concentration were determined, using decentralized processing of the signals of multiple sensors. Main emphasis is put on the local interfacial area concentration, here defined as the ratio of the total surface area of all bubbles in a reference volume to the size of that volume. The calculation of the surface area was based not only on the assumption of spherical bubbles, as is commonly done for bubbly flow, but on different bubble shapes. The calculated distribution of bubble sizes depends on the chord length resulting from the product of measured bubble velocity and bubble residence time at the sensor tip. The values for the interfacial area concentration for flows with low void fractions (α < 0.04) agree well with those measured by assuming only spherical bubbles. The existing deviations for flows with void fractions above α = 0.04 seem reasonable according to the differently assumed bubble shapes in the determination methods. This leads to an increase in the values for the interfacial area concentration.

Local Measurements in the Two-Phase Region of Turbulent Subcooled Boiling Flow

Local measurements of vapor phase residence time fraction, vapor bubble size distribution, bubble axial velocity, and vapor and liquid temperatures were performed in turbulent boiling flow of Refrigerant-113. The dissolved air content of the experimental fluid was minimized. Data are reported for three wall heat fluxes, two fluid mass velocities, and three subcoolings at test section inlet. Local time-averaged interfacial area concentrations were estimated. The measuring devices, viz., dual-sensor fiber-optic probe for the vapor bubble measurements and phase-compensated chromel-alumel microthermocouple for the fluid temperature measurement, provided more complete and accurate data compared with our earlier work. The data should be helpful in the development and validation of multidimensional turbulent boiling flow models. Further work is needed, however, before the local interfacial area concentration can be determined with confidence.

Measurement and modeling of average void fraction, bubble size and interfacial area

The local void fraction, bubble size and interfacial area concentration for co-current air-water bubbly flow through a horizontal pipe of 50.3 mm internal diameter were investigated experimentally using the double-sensor resistivity probe method. The local and area-averaged void fractions and interfacial area concentrations were analyzed as a function of liquid and gas flow rates. These parameters were found to increase systematically with decreasing liquid flow and increasing gas flow. However, variations with the liquid flow were not as significant as with the gas flow. A consistent variation of the gas phase drift velocity and distribution parameter with the liquid flow rate was observed. It was demonstrated that presentation of the average void fraction in terms of flowing volumetric concentration was more appropriate for horizontal bubbly flow. Several bubble break-up mechanisms were discussed. It was concluded that average pressure fluctuations generated by the turbulent liquid fluctuations acting across a bubble diameter are the only mechanism which causes distortion of a bubble. Based on this force and the competing surface tension force, a theoretical model was developed for mean bubble size and interfacial area concentration. The theoretically predicted mean bubble size and interfacial area concentration were found to agree reasonably well with those measured by the double-sensor resistivity method.

Theory and measurement of local interfacial area using a four sensor probe in two-phase flow

A theoretical foundation of the measurement method for the time averaged local interfacial area using a four sensor resistivity probe is presented. Based on this theory, the four sensor resistivity probe was developed and employed to measure the interfacial velocity, local interfacial area concentration and void fraction in a vertical air-water cap bubbly flow. The four sensor probe measurements were checked against the global void measurement using a differential pressure. The results were very satisfactory. Theoretical profiles of the void fraction and interfacial area concentration were obtained using the pictures of cap bubbles. The theoretical predictions of the cap bubbles and the interfacial area concentration profiles compared very well with the four sensor data.

Local instant formulation of two-phase flow

The local instant formulation of mass, momentum and energy conservations of two-phase flow has been developed. Distribution, an extended notion of a function, has been introduced for this purpose because physical parameters of two-phase flow media change discontinuously at the interface and the Lebesgue measure of an interface is zero. Using a characteristic function of each phase, the physical parameters of two-phase flow have been defined as field quantities. In addition to this, the source terms at the interface are defined in terms of the local instant interfacial area concentration. Based on these field quantities, the local instant field equations of mass, momentum and total energy conservations of two-phase flow have been derived. Modification of these field equations gives the single field representation of the local instant field equations of two-phase flow. Neglecting the interfacial force and energy, this formulation coincides with the field equations of single-phase flow, except in the definition of differentiation. The local instant two-fluid formulation of two-phase flow has also been derived. This formulation consists of six local instant field equations of mass, momentum and total energy conservations of both phases. Interfacial mass, momentum and energy transfer terms appear in these equations, which are expressed in terms of the local instant interfacial area concentration.

Local formulation and measurements of interfacial area concentration in two-phase flow

The interfacial area concentration is one of the most important parameters in analyzing two-phase flow based on the two-fluid model. The local instantaneous formulation of the interfacial area concentration is introduced here. Based on this formulation, time and spatial averaged interfacial area concentrations are derived, and the local ergodic theorem (the equivalency of the time and spatial averaged values) is obtained for stationary developed two-phase flow. On the other hand, the global ergodic theorem is derived for general two-phase flow. Measurement methods are discussed in detail in relation to the present analysis. The three-probe method, with which local interfacial area concentration can be measured accurately, has been proposed. The one-probe method under some statistical assumptions has also been proposed. In collaboration with the experimental data for the interfacial velocity, radial profiles of the local interfacial area concentration are obtained based on the one-probe method. The result indicates that the local interfacial area concentration has a peak value near the tube wall in bubbly flow. This is consistent with the near wall peak of local void fraction separately observed. In slug flow it shows a higher value in the central region of the tube for that particular set of data.