Two-phase Flow Situations Research Articles

Analysis of thin film thickness determination in two-phase flow using a multifiber optical sensor

Simulation studies had been conducted utilizing the principle of virtual image and vector analysis to demonstrate the possibility of using a multifiber optic sensor to determine the thickness and orientation (i.e., the liquid surface inclination angles) of a clear liquid film in a gas-liquid two-phase flow situation. The sensor system consists of a central light emitting fiber which is surrounded symmetrically by six light receiving fibers. By analyzing the different patterns of light intensity reflected back at the gas-liquid interface and collected by the six receiving fibers, the thin film thickness and its orientation with respect to the measuring point can be determined. The present study suggests that the sensor is capable of measuring liquid thin film thicknesses, including orientation relative to the measuring point, within the range of 0.54–4 mm. The limitation is mainly imposed by the numerical aperture of the optic fiber used.

Characteristics of Vertical Annular Two-Phase Flow with Local Liquid Fall-Back.

A new analytical method for two-phase flow is proposed, in which the most easily occurring and, thus, most stable two-phase flow situation is assumed to be realized. Flow structure is considered to be self-controlled so as to realize the most stable two-phase flow situation. In the present study, the flow situation with smaller pressure energy consumption rate for unit mass of penetrating two-phase fluid through each channel cross section is assumed to be more stable. In addition, two-dimensional turbulent flow analysis is applied to the annular flow regime in which partical or total downflow of the liquid film is allowed. Experimental analysis based on the data from an air-water two-phase flow experiment, which was performed at atmospheric pressure and room temperature, indicated the applicability of the proposed analytical method.

High pressure optical measurements of sizes, velocities and longitudinal positions of bubbles

This paper presents an optical system for taking shadow photographs of bubbles in a high-pressure evaporator tube. With this system and interpretation principles, not only the size and velocity of a bubble can be calculated from its shadow images on photos, but also its longitudinal position on the optical axis may be estimated from the size of a “bright spot” in its shadow image. A simple relation based on geometrical optics is applied. Performance of the new system and validity of the interpretation principles were examined through three series of calibration tests. Relative deviations of estimations to actual values of sizes and longitudinal positions of bubbles are within 1 and 5% respectively. Application at high-pressure was successful. Due to the general nature of the system and the interpretation principles, results may be extended to more dispersed two-phase flow situations.

A more general cell model for added mass in two-phase flow

The issue of added mass has often been misinterpreted and it is an important issue in the context of modeling bubbly flows where the added mass of the fluid dominates the inertia associated with bubble acceleration. This paper constitutes a thorough effort at identifying the forms the added mass coefficient, C, can take under various conditions. The paper can be divided into two sections: the first generalizes the cell model used by Zuber (1964, Chem. Engng Sci. 19, 897–903) and obtains various forms of C relating to a parameter λ, the “external impedance”. The versions of C suggested by Zuber (1964) and Wallis (1989, Multiphase Sci. Technol. 5, 239–361) become two limiting cases; the second develops an argument in terms of the equation of motions due to Wallis (1989) to arrive at the added mass, and its dependence on the boundary conditions. For the few sample cases studied, the characteristics of boundaries are found to be described by λ. Therefore, a general link between the added mass in various two-phase flow situations and one sphere moving inside a concentric shell is established.

Toward an improved description of the physics of two-phase flow

The present work incorporates the effects of interface dynamics into the theoretical description of two-phase flow in a porous medium. This advance offers the potential for improved understanding and modeling of multiphase flow processes. To provide background for this work, the traditional approach to describing two-phase flow in porous media is reviewed. The universally employed empirical extension of Darcy's Law for single-phase flow to two-phase flow situations is rejected as arbitrary and subject to severe shortcomings. Burial of dynamic effects into relative permeability and capillary pressure hysteresis is shown to be an unsatisfactory theoretical construct for modeling the actual processes occurring in two-phase flow. Examination of the traditional theory at equilibrium shows that interfacial forces actually present in multiphase systems have been overlooked causing the theory to provide contradictory results. To overcome these problems, a general theory of two-phase flow is proposed that is based on the basic principles of mass, momentum, and energy conservation and the second law of thermodynamics. This theory accounts, in a systematic way, for interfacial forces that are known to have an important effect on the movement of fluid phases in a porous medium. A new equation of momentum balance accounting for the presence of interfaces and their energetics is developed. This equation reduces to Darcy's Law for the special case of single-phase flow. The extended theory has the potential to describe phenomena unaccounted for by the traditional theory and thus provides a basis for scientific understanding of the physics of two-phase flow. Application of the theory requires experimental study to ascertain the values and precise functional dependence of the constitutive coefficients that arise.

Study of two-phase flow for a ramjet combustor

A reactive two-phase flow is studied experimentally by a special laser Doppler anemometry (LDA) technique and numerically by solving the elliptic governing equations. The relation between the liquid fuel injection and the aerodynamic flameholding mechanism of a dump combustor was investigated. The flow geometry chosen was an axisymmetric sudden expansion with small diameter ratio. The measurements included pressure, temperature, gas species concentration, as well as velocities of both phases and droplet size. A special processing technique enabled the simultaneous measurement of the gas velocity represented by the smallest droplets and of the size-velocity correlation of the droplets in the range of 5-500 |xm. The specific geometry of the sudden expansion combustor creates an annular flame stabilized just downstream of the step. The geometry of the flame depended very much on the equivalence ratio, with larger values creating longer and thicker flames. The combustion shortened the recirculation length from about 11 times the step height to about four times. There was no direct influence of the droplets on the average gas velocity in cold flow, whereas the size distribution of the droplets had significant influence on the combusting flow pattern. Two computational case studies were performed for isothermal and reactive two-phase flow situations. The numerical results indicated the fast dynamic and thermal response of the small droplets to the surrounding gas flow. Moreover, the droplets did not penetrate into the fuel-rich recirculation zone. The shear layer, which separates it from the core, was characterized by a local equivalence ratio close to unity. The numerical predictions and the experimental results exhibited fairly good agreement, provided that the initial conditions of the spray and the thermal boundary conditions are determined experimentally.

A comparison of initial conditions for continuous-flow systems

An initial condition, which sets the state of a system at a particular time, should describe accurately the physics of the situation and should not create computational artifacts when the governing equations are solved numerically. Drawing on the example of two-phase flow in porous media, we show that unphysical oscillations can mar a solution should the initial condition violate an inflow boundary condition. Tracking these oscillations can increase by orders of magnitude the computer time needed to solve the equations of change. At an internal boundary between two different media, an initial condition that violates the steady-state equations of change produces features that might be equally undesirable. We propose a way to generate initial conditions that avoid these artifacts, viz. by splicing together a solution of the linearized governing equations in the region of change and solutions of the steady-state equations in regions of constancy. We demonstrate our proposal using the situation of two-phase flow in porous media. Our findings are broadly applicable because of the partial analogies among transport of mass, heat and momentum.

Flow of bubbles through nozzles

One of the fundamental objectives in the mathematical modeling of two-phase flow is to understand and to formulate the interaction forces between two phases. For this purpose a well-defined two-phase flow situation, flow of bubbles through nozzles, was set up in the laboratory. A range of liquid flow fields was set up by flowing water through nozzles. Individual bubbles were injected into the water stream and their trajectories were recorded to provide data for evaluation and comparison with theories. Because of the limitations of the conventional photographic method of recording the bubble path, a computer-based optical system was designed for fast data acquisition. The optimal system works on the principle of the interruption of a light beam by a bubble passing between a sheet of light and a row of phototransistors. The bubble position (horizontal as well as vertical) along the nozzle is determined by its crossing through the light path to several rows of phototransistors attached to the nozzle. The performance and accuracy of the optical system were tested under various known physical situations. All the tests showed that the optical system is competent and effective in studying the motion of bubbles flowing through nozzles. A mathematical model was set up to predict the bubble motion. The various forces included in the model are the drag force, the apparent mass force, the buoyancy force, the bubble expansion force and the history forces. Comparisons between experiments and theories were made through a “point-to-point” numerical testing procedure. Results show that the bubble trajectory can be reasonably predicted (within 10% accuracy) by an equation of motion which includes a suitable drag force (dependent on relative velocity) and an apparent mass force (proportional to relative acceleration). Suggestions regarding the further improvement of the theory are also made.

On the application of an “entropy maximizing principle” in flow regime predictions

The validity of the “theorem” of minimum entropy production (per unit time) is assessed for the well documented case of single-phase fluid tube flow bifurcations from laminar to turbulent regimes, with and without external heat exchange. The analysis leads to the following main conclusions. (1): This “theorem” is not generally valid. (2): The stable type of flow regime is associated with a maximum specific (per unit mass) entropy change. The second conclusion provides additional empirical support for the analytical methods based on an “entropy maximizing principle” proposed by several researchers to predict stable flow regimes and/or void fractions in highly complex two-phase flow situations.

Transition from stratified to slug regime in countercurrent flow

In many two-phase flow situations the prediction on the conditions likely to instigate the change of flow pattern from the stratified regime to the slug flow condition is important. Since published material on such predictions for countercurrent flow is scarce this paper considers the influencing parameters for these conditions and then uses the data recorded from an experimental test rig to quantify the developed instability criterion equation.

Pseudoskin Factor Caused by Partial Penetration

Pseudoskin Factor Caused by Partial Penetration

An Analytic Solution for the Void Fraction During Simultaneous Linear Pressure Decay and Exponential Inlet Velocity Decay in a Diabatic Channel

An approximate analytical solution is presented for the spatial and temporal distribution, in a uniformly heated channel, of the void fraction for exponentially decaying inlet velocity and for a linear time-rate-of change of system pressure. The solution, in addition to increasing the extremely limited number of analytic solutions for non-steady non-homogeneous two-phase flows, allows their use in a hybrid prediction technique to explore some complex two-phase flow situations with a minimum of computation effort and expense.