A high frequency electronic transducer for multiphase flow measurements

This paper describes an electronic transducer for multiphase flow measurement. Its high sensitivity, good signal to noise ratio and accuracy are achieved through an electrical impedance sensor with a special guard technique. The transducer consists of a wide bandwidth and high slew rate differentiator where the lead inductance and stray capacitance effects are compensated. The sensor edge effect is eliminated by using a guard electrode based on the virtual ground potential of the operational amplifier. A theoretical modeling and a calibration method are also presented. The results obtained seem to confirm the validity of the proposed technique.

Modeling of turbulent flow through radial diffuser

The work considers the modeling of turbulent flow in radial diffuser with axial feeding. Due to its claimed capability to predict flow including features such as separation, curvature and adverse pressure gradient, the RNG k-epsilon model of Orzag et al. (1993) is applied in the present analysis. The governing equations are numerically solved using the finite volume methodology. Experiments were conducted to assess the turbulence model. Numerical results of pressure distribution on the front disk surface for different flow conditions when compared to the experimental data indicated that the RNG k-epsilon model is adequate to predict this class of flow.

Turbulent heat transfer and pressure drop in pinned annular regions

Experiments were performed to determine average heat transfer coefficients and friction factors for turbulent flow through annular ducts with pin fins. The measurements were carried out by means of a double-pipe heat exchanger. The total number of pins attached to the inner wall of the annular region was 560. The working fluids were air, flowing in the annular channel, and water through the inner circular tube. The average heat transfer coefficients of the pinned air-side were obtained from the experimental determination of the overall heat transfer coefficients of the heat exchanger and from the knowledge of the average heat transfer coefficients of the circular pipe (water-side), which could be found in the pertinent literature. To attain fully developed conditions, the heat exchanger was built with additional lengths before and after the test section. The inner circular duct of the heat exchanger and the pin fins were made of brass. Due to the high thermal conductivity of the brass, the small tube thickness and water temperature variation, the surface of the internal tube was practically isothermal. The external tube was made of an industrial plastic which was insulated from the environment by means of a glass wool batt. In this manner, the outer surface of the annular channel can be considered adiabatic. The results are presented in dimensionless forms, in terms of average Nusselt numbers and friction factors as functions of the flow Reynolds number, ranging from 13,000 to 80,000. The pin fin efficiency, which depends on the heat transfer coefficient, is also determined as a function of dimensionless parameters. A comparison of the present results with those for smooth sections (without pins) is also presented. The purpose of such a comparison is to study the influence of the presence of the pins on the pressure drop and heat transfer rate.

Static pressure and wall shear stress distributions in air flow in a seven wire-wrapped rod bundle

An experimental investigation is performed in a turbulent flow in a seven wire-wrapped rod bundle, mounted in an open air facility. Static pressure distributions are measured on central and peripheral rods. By using a Preston tube, the wall shear stress profiles are experimentally obtained along the perimeter of the rods. The geometric parameters of the test section are P/D=1.20 and H/D=15. The measuring section is located at L/D=40 from the air inlet. It is observed that the dimensionless static pressure and wall shear stress profiles are nearly independent of the Reynolds number and strongly dependent of the wire-spacer position, with abrupt variations of the parameters in the neighborhood of the wires.

Numerical study on mixed convection in a horizontal flow past a square porous cavity using UNIFAES scheme

Mixed convection on the flow past a heated length and past a porous cavity located in a horizontal wall bounding a saturated porous medium is numerically simulated. The cavity is heated from below. The steady-state regime is studied for several intensities of the buoyancy effects due to temperature variations. The influences of Péclet and Rayleigh numbers on the flow pattern and the temperature distributions are examined. Local and global Nusselt numbers are reported for the heated surface. The convective-diffusive fluxes at the volume boundaries are represented using the UNIFAES, Unified Finite Approach Exponential-type Scheme, with the Power-Law approximation to reduce the computing time. The conditions established by Rivas for the quadratic order of accuracy of the central differencing to be maintained in irregular grids are shown to be extensible to other quadratic schemes, including UNIFAES, so that accuracy estimates could be obtained.

Experimental analysis of pressure drop and flow redistribution in axial flows in rod bundles

Fuel elements of PWR type nuclear reactors consist of rod bundles, arranged in a square array, and held by spacer grids. The coolant flows, mainly, axially along the rods. Although such elements are laterally open, experiments are performed in closed type test sections, originating the appearance of subchannels with different geometries. In the present work, utilizing a test section of two bundles of 4x4 pins each, experiments were performed to determine the friction and the grid drag coefficients for the different subchannels and to observe the effect of the grids in the crossflow, in cases of inlet flow maldistribution.

An experimental investigation of the effects of nozzle ellipticity on the flow structure of co-flow jet diffusion flames

The flow structure of cold and ignited jets issuing into a co-flowing air stream was experimentally studied using a laser Doppler velocimeter. Methane was employed as the jet fluid discharging from circular and elliptic nozzles with aspect ratios varying from 1.29 to 1.60. The diameter of the circular nozzle was 4.6 mm and the elliptic nozzles had approximately the same exit area as that of the circular nozzle. These non-circular nozzles were employed in order to increase the stability of attached jet diffusion flames. The time-averaged velocity and r.m.s. value of the velocity fluctuation in the streamwise and transverse directions were measured over the range of co-flowing stream velocities corresponding to different modes of flame blowout that are identified as either lifted or attached flames. On the basis of these measurements, attempts were made to explain the existence of an apparent optimum aspect ratio for the blowout of attached flames observed at higher values of co-flowing stream velocities. The insensitivity of the blowout limits of lifted flames to nozzle geometry observed in our previous work at low co-flowing stream velocities was also explained. Measurements of the fuel concentration at the jet centerline indicated that the mixing process was enhanced with the 1.38 aspect ratio jet compared with the 1.60 aspect ratio jet. On the basis of the obtained experimental data, it was suggested that the higher blowout limits of attached flames for an elliptic jet of 1.38 aspect ratio was due to higher entrainment rates.

Gas-solid two-phase flow in the riser of circulating fluidized beds: mathematical modelling and numerical simulation

A mathematical model is developed for gas-solids flows in circulating fluidized beds. An Eulerian formulation is followed based on the two-fluids model approach where both the fluid and the particulate phases are treated as a continuum. The physical modelling is discussed, including the formulation of boundary conditions and the description of the numerical methodology. Results of numerical simulation are presented and discussed. The model is validated through comparison to experiment, and simulation is performed to investigate the effects on the flow hydrodynamics of the solids viscosity.

Chaos and Unpredictability in the Vibration of an Elasto-Plastic Beam

This contribution discusses the nonlinear dynamics of a pin-ended elasto-plastic beam with both kinematic and isotropic hardening. An iterative numerical procedure based on the operator split technique is developed in order to deal with the nonlinearities in the equations of motion. Free and forced responses for harmonic sinusoidal and square wave excitations are investigated. Numerical simulations present many interesting behaviors such as jump phenomena, sensitivity to initial conditions, chaos and transient chaos. These results indicate that there are practical problems in predicting the response of the beam even when periodic steady state response is expected.

Two-Phase (Solid-Liquid) Flow in Inclined Pipes

This paper presents an experimental research about the behavior of two-phase flows in inclined pipes. The inclination angle varied from 5° to 45° and the slurry solid concentration varied up to 15%. It was concluded that the head losses of the downward sloping pipe flow are always lower than the head losses of the horizontal flow and these are always lower than the head losses of the upward sloping pipe flow, regardless the concentration and inclination angle. It was possible to develop empirical equations to calculate the head losses of the horizontal flow and the upward and downward sloping pipe flows.

Panel Method Formulation for Oscillating Airfoils in Sonic Flow

The mathematical model for two-dimensional unsteady sonic flow, based on the classical diffusion equation with imaginary coefficient, is presented and discussed. The main purpose is to develop a rigorous formulation in order to bring into light the correspondence between the sonic, supersonic and subsonic panel method theory. Source and doublet integrals are obtained and Laplace transformation demonstrates that, in fact, the source integral is the solution of the doublet integral equation. It is shown that the doublet-only formulation reduces to a Volterra integral equation of the first kind and a numerical method is proposed in order to solve it. To the authors' knowledge this is the first reported solution to the unsteady sonic thin airfoil problem through the use of doublet singularities. Comparisons with the source-only formulation are shown for the problem of a flat plate in combined harmonic heaving and pitching motion.

Bubble-Bubble Interaction in Horizontal Two-Phase Slug Flow

Modelling of the slug structure requires a new effort on fundamental research. To clarify some aspects of the horizontal slug flow, an experimental study of the behaviour of two isolated bubbles in a single-phase liquid flow was performed. This procedure was adopted to avoid the overlap of different phenomena induced by a train of long bubbles. The experimental facility consists of a 90-m horizontal PVC pipe with internal diameter of 0,053 m. The behaviour of two single air bubbles travelling in a water flow was studied. Focus was given on the influence of the distance between the bubbles on the velocity of the second bubble. This study allows the understanding of the mechanism of overtaking that takes place right after the slug formation and that precedes the coalescence of bubbles in a slug flow. The results show that bubbles placed behind a liquid slug smaller than a critical value move faster than the leading one. Otherwise, they move slower than the leading one.

Horizontal Slug Flow in a Large-Size Pipeline: Experimentation and Modeling

The knowledge of the slug flow characteristics is very important when designing pipelines and process equipment. When the intermittences typical in slug flow occurs, the fluctuations of the flow variables bring additional concern to the designer. Focusing on this subject the present work discloses the experimental data on slug flow characteristics occurring in a large-size, large-scale facility. The results were compared with data provided by mechanistic slug flow models in order to verify their reliability when modelling actual flow conditions. Experiments were done with natural gas and oil or water as the liquid phase. To compute the frequency and velocity of the slug cell and to calculate the length of the elongated bubble and liquid slug one used two pressure transducers measuring the pressure drop across the pipe diameter at different axial locations. A third pressure transducer measured the pressure drop between two axial location 200 m apart. The experimental data were compared with results of Camargo's1 algorithm (1991, 1993), which uses the basics of Dukler & Hubbard's (1975) slug flow model, and those calculated by the transient two-phase flow simulator OLGA.

Pressure Drop in Vertical Core-Annular Flow

An experimental apparatus for the study of core annular flows of heavy oil and water at room temperature has been set up and tested at laboratory scale. The test section consists of a 2.75 cm ID galvanized steel pipe. Tap water and a heavy oil (17.6 Pa.s; 963 kg/m³) were used. Pressure drop in a vertical upward test section was accurately measured for oil flow rates in the range 0.297 - 1.045 l/s and water flow rates ranging from 0.063 to 0.315 l/s. The oil-water input ratio was in the range 1-14. The measured pressure drop comprises gravitational and frictional parts. The gravitational pressure drop was expressed in terms of the volumetric fraction of the core, which was determined from a correlation developed by Bannwart (1998b). The existence of an optimum water-oil input ratio for each oil flow rate was observed in the range 0.07 - 0.5. The frictional pressure drop was modeled to account for both hydrodynamic and net buoyancy effects on the core. The model was adjusted to fit our data and shows excellent agreement with data from another source (Bai, 1995).

Flows of Bingham Materials Through Ideal Porous Media: an Experimental and Theoretical Study

The flow of Bingham liquids through porous media has been studied. Experiments have been performed to determine the flow rate / pressure drop relationship for the flow of a grease of Binghamian rheological behavior through an array of rods of circular cross section. The yield stress and plastic viscosity of the grease have been determined with the aid of a controlled stress rotational rheometer. To investigate a wider range of the flow parameters, the mass and momentum conservation equations have been solved numerically, in conjunction with the generalized Newtonian constitutive law and the bi-viscosity model. The finite volume method has been employed to obtain the numerical solution. These numerical results also yielded a flow rate / pressure drop relationship, which is in very good agreement with the experimental results. A capillaric theory has been developed to determine an analytical relationship between the flow rate and pressure drop for flows of Bingham liquids through porous media. It is shown that the predictions of this theory are in good agreement with the experimental and numerical results.