Liquid Mass Flux Research Articles

Mass Transfer during gas absorption from a linear cluster of slugs in the presence of inert gases

A model of mass transfer during isothermal gas absorption in the presence of inert gas from a slug rising in a channel filled with liquid is suggested. The work studies the case of a small amount of soluble gas inside a slug and employs the approximation of a thin concentration boundary layer. Theoretical results of mass transfer analysis for a single gas slug are applied for determination of mass transfer rate in gas liquid slug flow. In the assumption of a perfect mixing of the dissolved gas in liquid plugs, recurrent relations for the dissolved gas concentration in the n-th liquid plug and mass flux from the n-th gas slug are derived. The mass transfer coefficient in gas-liquid slug flow is determined. In the limiting case the derived formulas for mass transfer in the presence of inert admixtures recover the obtained expressions for mass transfer during absorption of a pure gas. Theoretical results are compared with available experimental data.

Structure and mixing properties of combusting monopropellant sprays

The spray combustion properties of a hydroxylammonium nitrate (HAN)-based monopropellant (LGP 1845) were studied both theoretically and experimentally. Drop size, liquid mass flow rate, and liquid mass flux distributions were measured for pressure-atomized sprays in the atomization breakup regime, burning within a combustion gas environment at pressures of 4.5-5.0 MPa. Two separated-flow models were evaluated using the new measurements: a deterministic separated-flow model where drop-turbulence interactions were ignored, and a stochastic separated-flow model where drop-turbulence interactions were considered using random-walk computations for drop motion. When based on burning rates found from earlier single-drop experiments, both models were in reasonably good agreement with the measurements. Separated-flow effects are quite important for these sprays, with the length of the liquid-containing region being relatively independent of injector diameter and extending roughly 300 mm from the injector exit for injector exit velocities of roughly 70 m/s and injector diameters of 0.3 and 0.6 mm.

Analysis of direct liquid-solid contact heat transfer in monodispersed spray cooling

The heat-transfer characteristics of a single droplet and spray impacting upon a horizontal surface heated above the Leidenfrost temperature are analytically investigated. The heat-transfer model of a single impacting droplet is developed, based on the postulate that heat transfer through direct contact is the dominant mechanism of the droplet impacting heat transfer. Heat-transfer models of spray are also developed by expanding the single droplet model to include the effects of droplet interference upon the impacting dynamics. A criterion value of liquid mass flux for classifying a spray as sparse or dense is established. The analytical models are compared with the existing experimental results, and they are found to be in good agreement.

Drop size measurements for annular two-phase flow in a 20 mm diameter vertical tube

As part of a study on the effect of tube diameter on the mean drop size and liquid film flow rate in annular two-phase flow, data was obtained for the vertical upflow of an air-water system in a 20 mm internal diameter tube, held at a pressure of 1.5 bar and ambient temperature. This complements data taken in earlier experiments on 10 and 32 mm tubes. Increases in the superficial gas velocity caused reductions in the mean drop size whilst increasing the liquid mass flux in all but the lowest gas velocity case, caused the drop size to rise. Comparisons were made between the current drop size data and that from a 10 mm and 32 mm internal diameter tube, for similar conditions of temperature and pressure. The current drop size measurements, which fall between those from earlier work, confirm the dependence of drop size on tube diameter. The performance of several drop size correlations have been tested. Because the correlations do not account for the influence of tube diameter, they fail to predict the drop size data accurately. The influence of gas and liquid flow rate on the measured film flow rate show trends similar to those seen in data from the 10 mm and 32 mm diameter tubes. Models, to calculate the entrained liquid mass flux were tested; good predictions were given.

Heater probe technique to measure flow maldistribution in large scale trickle bed reactors

Novel flow distribution measurement probes were used in a large-scale commercially operating trickle-bed reactor. The probes consist of long heated pipes designed to measure local heat transfer coefficients at multiple points along their length. Local flow rates are correlated with the heat transfer coefficient based on independent laboratory data. The results of our study showed significant point-to-point variation in flow distribution. The pattern of maldistribution would vary with alternate operating conditions of flow rates, temperature, and liquid volatility. Results included an increase in the nonuniformity of flow moving down the reactor in the direction of flow. And severe maldistribution with poor reactor performance occurred at high liquid mass flux.

Analysis on film boiling heat transfer of impacting sprays

The analysis on film boiling of impacting sprays is separated into two cases—a dilute spray (negligible heat transfer interaction among droplets) and a dense spray (significant interaction). The heat transfer of an impacting dilute spray is analyzed by dividing the mechanisms into three identified subprocesses—drop contact heat transfer, bulk air convective heat transfer and radiative heat transfer. Both horizontal and vertical sprays are modeled. The predictions are very satisfactory. For the dense spray film boiling, the asymptotic approach is successful. The low end asymptote corresponds to the dilute spray situation while the high end asymptote is adequately represented by the pool boiling situation for most spray conditions. The liquid mass flux is the most dominant parameter in both cases. Dense spray film boiling is found to show very little dependence on droplet parameters; however, dilute spray film boiling is significantly influenced by droplet parameters.

Transient laminar-film condensation on a vertical plate

This work addresses the problem of transient, laminar-film condensation onto a vertical surface. It examines the behavior of the liquid film in response to changes in the temperature drop across the film or in the interfacial shear stress. Numerical solutions of the governing equations are compared with a simpler quasisteady analysis. The quasisteady analysis is adequate in many cases (e.g., atmospheric water). However, as the Jakob number or Jakob divided by Prandtl number approaches unity, the full equations and the quasisteady analysis yield significantly different predictions for heat transfer and mass flux during the transient. This reflects the increasing importance of accounting for the development of the temperature and velocity profiles. Nomenclature Cp = liquid specific heat D2 = finite-difference form of the Laplacian operator g = gravitational acceleration hfg = latent heat of vaporization Ja = Jakob number, Cp AT+ /hfg k = liquid thermal conductivity L = plate length Pr = liquid Prandtl number, v/a q = interfacial heat flux T = temperature t = time u = streamwise velocity v = cross-stream velocity x = streamwise coordinate y = cross-stream coordinate a = liquid thermal diffusivity T = liquid mass flux per unit width of plate d = film thickness d yy = film thickness at x + = L using Nusselt theory A = difference or increment fj. = liquid dynamic viscosity v = liquid kinematic viscosity p = liquid density i = interfacial shear stress

Heat transfer experiments of mono-dispersed vertically impacting sprays

The heat transfer of vertically impacting water sprays has been investigated experimensally using a one-dimensional mono-size spray. The liquid mass flux, droplet size and droplet velocity of the spray are independently variable in ranges. At low liquid flux, the film boiling heat transfer of an impacting spray is affected by the droplet size and velocity; however, at high liquid flux these effects become much less observable. The contribution of air convection to the overall heat transfer is low. The dominant parameter affecting the impacting spray heat transfer is the liquid mass flux. The film boiling heat transfer of impacting sprays has a power-law dependency on the liquid mass flux with the power varying from unity to a fraction as the liquid mass flux is increased.

Mechanisms of film boiling heat transfer of normally impacting spray

The heat transfer mechanisms of horizontally impacting sprays were studied experimentally. An impulse-jet liquid spray system and a solid particle spray system were used. The liquid spray system is capable of producing uniform droplets with the independent variables of droplet size, velocity, liquid flow rate, and air velocity. The horizontally impacting sprays give a lower heat transfer at film boiling than the corresponding vertically impacting spray. The film boiling heat transfer is mainly controlled by the liquid mass flux. At low liquid mass flux and low droplet Weber number, the heat transfer increases with the droplet Weber number. At high droplet Weber number or high liquid mass flux, the heat transfer is not significantly affected by the droplet Weber number.

Studies of Flows Through N-Sequential Orifices

Critical mass flux and axial pressure profile data for fluid nitrogen are presented for N = 20, 15, 10, and 7 N-sequential-orifice-inlet configurations uniformly spaced at 15.5 cm. These data correlate well over a wide range in reduced temperature (0.7 < Tr, 0 < ambient) and reduced pressure (to Pr = 2) and are in general agreement with previous studies of one to four inlets. Experimental and theoretical agreement is good for liquid and gas critical mass flux, but inconclusive in the near-thermodynamic critical regions.

Experimental Modeling of Core Hydrodynamics during Reflood Phase of LOCA

The over-all core hydrodynamics during the reflood phase is quantitatively discussed. The following model was proposed for the core hydrodynamics: (1) When the liquid mass flux and the steam mass flux exist at the quench front, dispersed flow appears. (2) The void fraction downstream of the quench front gradually decreases with time. (3) Finally, the void fraction approaches the value predicted by the modified Cunningham & Yeh and the modified Lockhart-Martinelli correlations within about ±30% error. (4) Even after the concerning region is quenched, the void fraction can be predicted with the same correlations. Both correlations have been recently developed.

Transient Melting of a Solid Heated by a Condensing Saturated Vapor—Case I: Negligible Interface Curvature

A transient analysis has been performed to analytically determine the instantaneous dimensionless thickness of a vertically suspended solid at its melting temperature upon which a saturated vapor is condensing. The spatial variation and transient behavior of the melt-condensate liquid film, which is continuously drained, has also been obtained from the closed form analytical solution of the uncoupled equations for the solid-liquid and liquid-vapor interface motions under the condition of assumed negligible interface curvature. Classical boundary layer assumptions were applied to the convection process in the subcooled liquid film which was analyzed using integral techniques. From the analytic solution to the resultant interface motion equations in terms of characteristic curves, the functional dependence of the melting solid and the liquid layer thicknesses on the time and space variables was established. The liquid mass flux and heat transfer coefficient were then obtained analytically.