On the accuracy of two-fluid model predictions for a particular gas-solid riser flow

Literature presents a huge number of different simulations of gas-solid flows in risers applying two-fluid modeling. In spite of that, the related quantitative accuracy issue remains mostly untouched. This state of affairs seems to be mainly a consequence of modeling shortcomings, notably regarding the lack of realistic closures. In this article predictions from a two-fluid model are compared to other published two-fluid model predictions applying the same Closures, and to experimental data. A particular matter of concern is whether the predictions are generated or not inside the statistical steady state regime that characterizes the riser flows. The present simulation was performed inside the statistical steady state regime. Time-averaged results are presented for different time-averaging intervals of 5, 10, 15 and 20 s inside the statistical steady state regime. The independence of the averaged results regarding the time-averaging interval is addressed and the results averaged over the intervals of 10 and 20 s are compared to both experiment and other two-fluid predictions. It is concluded that the two-fluid model used is still very crude, and cannot provide quantitative accurate results, at least for the particular case that was considered. (C) 2009 Elsevier Inc. All rights reserved.

Hybrid modeling of convective laminar flow in a permeable tube associated with the cross-flow process

The confined flows in tubes with permeable surfaces arc associated to tangential filtration processes (microfiltration or ultrafiltration). The complexity of the phenomena do not allow for the development of exact analytical solutions, however, approximate solutions are of great interest for the calculation of the transmembrane outflow and estimate of the concentration, polarization phenomenon. In the present work, the generalized integral transform technique (GITT) was employed in solving the laminar and permanent flow in permeable tubes of Newtonian and incompressible fluid. The mathematical formulation employed the parabolic differential equation of chemical species conservation (convective-diffusive equation). The velocity profiles for the entrance region flow, which are found in the connective terms of the equation, were assessed by solutions obtained from literature. The velocity at the permeable wall was considered uniform, with the concentration at the tube wall regarded as variable with an axial position. A computational methodology using global error control was applied to determine the concentration in the wall and concentration boundary layer thickness. The results obtained for the local transmembrane flux and the concentration boundary layer thickness were compared against others in literature. (C) 2007 Elsevier B.V. All rights reserved.

Stability analysis of core-annular flow and neutral stability wave number

A general transition criterion is proposed in order to locate the core-annular flow pattern in horizontal and vertical oil-water flows. It is based on a rigorous one-dimensional two-fluid model of liquid-liquid two-phase flow and considers the existence of critical interfacial wave numbers related to a non-negligible interfacial tension term to which the linear stability theory still applies. The viscous laminar-laminar flow problem is fully resolved and turbulence effects on the stability are analyzed through experimentally obtained shape factors. The proposed general transition criterion includes in its formulation the inviscid Kelvin-Helmholtz`s discriminator. If a theoretical maximum wavelength is considered as a necessary condition for stability, a stability criterion in terms of the Eotvos number is achieved. Effects of interfacial tension, viscosity ratio, density difference, and shape factors on the stability of core-annular flow are analyzed in detail. The more complete modeling allowed for the analysis of the neutral-stability wave number and the results strongly suggest that the interfacial tension term plays an indispensable role in the correct prediction of the stable region of core-annular flow pattern. The incorporation of a theoretical minimum wavelength into the transition model produced significantly better results. The criterion predictions were compared with recent data from the literature and the agreement is encouraging. (C) 2007 American Institute of Chemical Engineers.

Stepped and smooth spillways: resistance effects on stilling basin lengths

The Darcy-Weisbach equation was used in the analysis of flow over spillways, furnishing theoretical tools to design stilling basins. Predictions for the length of hydraulic jump stilling basins downstream of stepped and smooth spillways are presented, together with ranges of values for the Darcy-Weisbach friction factor of both spillways. The experimental data were compared with results of the theoretical solution of the gradually varied flow equation. All comparisons were made in non-dimensional form. The values of the Darcy-Weisbach friction factor were roughly five times smaller for smooth spillways than for stepped spillways. The theoretical predictions and the experimental data allow to present approximate equations for a preliminary evaluation of the length and the bed level of hydraulic jump stilling basins. In the same way, approximate equations were presented for the evaluation of the friction factor in smooth and stepped spillways, as a function of the Froude number at the downstream cross-section.

Assessment of groundwater recharge and water fluxes of the Guarani Aquifer System, Brazil

The groundwater recharge and water fluxes of the Guarani Aquifer System in the state of Sao Paulo in Brazil were assessed through a numeric model. The study area (6,748 km(2)) comprises Jacar,-Gua double dagger A(0) and Jacar,-Pepira River watersheds, tributaries of the Tiet River in the central region of the state. GIS based tools were used in the storage, processing and analysis of data. Main hydrologic phenomena were selected, leading to a groundwater conceptual model, taking into account the significant outcrops occurring in the study area. Six recharge zones were related to the geologic formation and structures of the semi-confined and phreatic aquifer. The model was calibrated against the baseflows and static water levels of the wells. The results emphasize the strong interaction of groundwater flows between watersheds and the groundwater inflow into the rivers. It has been concluded that lateral groundwater exchanges between basins, the deep discharges to the regional system, and well exploitation were not significant aquifer outflows when compared to the aquifer recharge. The results have shown that the inflows from the river into the aquifer are significant and have the utmost importance since the aquifer is potentially more vulnerable in these places.

Friction loss correction in flowing well discharge tests

Artesian confined aquifers do not need pumping energy, and water from the aquifer flows naturally at the wellhead. This study proposes correcting the method for analyzing flowing well tests presented by Jacob and Lohman (1952) by considering the head losses due to friction in the well casing. The application of the proposed correction allowed the determination of a transmissivity (T = 411 m(2)/d) and storage coefficient (S = 3 x 10(-4)) which appear to be representative for the confined Guarani Aquifer in the study area. Ignoring the correction due to head losses in the well casing, the error in transmissivity evaluation is about 18%. For the storage coefficient the error is of 5 orders of magnitude, resulting in physically unacceptable value. The effect of the proposed correction on the calculated radius of the cone of depression and corresponding well interference is also discussed.

Air uptake along the lower nappe of a spillway aerator

Air concentration measurements performed along the lower nappe of a bottom aerator through the impact and downstream flow regions permitted the calculation of air entrainment along the jet length. The air uptake was also measured in the air supply conduit. It was shown that integration of the concentration profiles along the jet overestimates the air uptake measured in the air supply conduit. Corrective procedures were developed by adapting the concept of entrained and entrapped air, in which the latter is re-circulated in the cavity, but both are measured by air concentration probes.

Slip ratio in dispersed viscous oil-water pipe flow

In this article, dispersed flow of viscous oil and water is investigated. The experimental work was performed in a 26.2-mm-i.d. 12-m-long horizontal glass pipe using water and oil (viscosity of 100 mPa s and density of 860 kg/m(3)) as test fluids. High-speed video recording and a new wire-mesh sensor based on capacitance (permittivity) measurements were used to characterize the flow. Furthermore, holdup data were obtained using quick-closing-valves technique (QCV). An interesting finding was the oil-water slip ratio greater than one for dispersed flow at high Reynolds number. Chordal phase fraction distribution diagrams and images of the holdup distribution over the pipe cross-section obtained via wire-mesh sensor indicated a significant amount of water near to the pipe wall for the three different dispersed flow patterns identified in this study: oil-in-water homogeneous dispersion (o/w H), oil-in-water non-homogeneous dispersion (o/w NH) and Dual continuous (Do/w & Dw/o). The phase slip might be explained by the existence of a water film surrounding the homogeneous mixture of oil-in-water in a hidrofilic-oilfobic pipe. (C) 2010 Elsevier Inc. All rights reserved.

Experimental study of a Tollmien-Schlichting wave interacting with a shallow 3D roughness element

The paper is devoted to an experimental study of the effect of a shallow 3D roughness element on the evolution of a 2D Tollmien-Schlichting wave in a Blasius boundary layer. The experiments were carried out under controlled disturbance conditions on an airfoil section which could provide a long run with zero pressure gradient flow. A pneumatically driven slit source was used to introduce the Tollmien-Schilichting wave upstream of the lower branch of the neutral stability curve. A few wavelengths downstream, the T-S wave interacts with a cylindrical roughness element. The height of the roughness was slowly oscillating in time, which allows a continuous measurement of the T-S wave response downstream the roughness. The oscillation frequency was approximately 1500 times lower than the frequency of the studied Tollmien-Schlichting wave and therefore, behaved as a steady roughness with respect to the T-S wave. Hot wire anemometry was used to measure wall normal profiles and spanwise scans close to the maximum of the eigenfunction of the T-S wave. The oscillation of the roughness and the synchronization of all-equipments permitted the use of ensemble average techniques. Two different amplitudes of T-S waves with a non-dimensional frequency of F120E-06 were studied. They show a strong amplification of the disturbances in a small spanwise wave number range. The analysis of the wall normal T-S profiles suggests the growth of oblique modes.

Debris flow affecting the Cubatauo Oil Refinery, Brazil

On February 6, 1994, a large debris flow developed because of intense rains in a 800-m-high mountain range called Serra do Cubatao, the local name for the Serra do Mar, located along the coast of the state of Sao Paulo, Brazil. It affected the Presidente Bernardes Refinery, owned by Petrobras, in Cubatao. The damages amounted to about US $40 million because of the muck cleaning, repairs, and 3-week interruption of the operations. This prompted Petrobras to conduct studies, carried out by the authors, to develop protection works, which were done at a cost of approximately US $12 million. The paper describes the studies conducted on debris flow mechanics. A new criteria to define rainfall intensities that trigger debris flows is presented, as well as a correlation of slipped area with soil porosity and rain intensity. Also presented are (a) an actual grain size distribution of a deposited material, determined by laboratory and a large-scale field test, and (b) the size distribution of large boulders along the river bed. Based on theory, empirical experience and back-analysis of the events, the main parameters as the front velocity, the peak discharge and the volume of the transported sediments were determined in a rational basis for the design of the protection works. Finally, the paper describes the set of the protection works built, emphasizing their concept and function. They also included some low-cost innovative works.

On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism

The mechanism of wake-induced vibrations (WIV) of a pair of cylinders in a tandem arrangement is investigated by experiments. A typical WIV response is characterized by a build-up of amplitude persisting to high reduced velocities; this is different from a typical vortex-induced vibration (VIV) response, which occurs in a limited resonance range. We suggest that WIV of the downstream cylinder is excited by the unsteady vortex-structure interactions between the body and the upstream wake. Coherent vortices interfering with the downstream cylinder induce fluctuations in the fluid force that are not synchronized with the motion. A favourable phase lag between the displacement and the fluid force guarantees that a positive energy transfer from the flow to the structure sustains the oscillations. If the unsteady vortices are removed from the wake of the upstream body then WIV will not be excited. An experiment performed in a steady shear flow turned out to be central to the understanding of the origin of the fluid forces acting on the downstream cylinder.

Wake instability issues: From circular cylinders to stalled airfoils

Some recent results regarding the global dynamical behaviour of the wake of circular cylinders and airfoils with massive separation are reviewed in this paper. In order to investigate the effect of interference, the three-dimensional instability modes are analysed for the flow around two circular cylinders in tandem. In the same way, the flow around a stalled airfoil is investigated in order to provide a better understanding of the three-dimensional characteristics of wakes forming downstream of a lifting body with massive separation. These results are compared with those found for an isolated cylinder. Some fundamental differences among these flows are discussed. (C) 2011 Elsevier Ltd. All rights reserved.

Floquet stability analysis of the flow around an oscillating cylinder

This investigative work is concerned with the flow around a circular cylinder submitted to forced transverse oscillations. The goal is to investigate how the transition to turbulence is initiated in the wake for cases with different Reynolds numbers (Re) and displacement amplitudes (A). For each Re the motion frequency is kept constant, close to the Strouhal number of the flow around a fixed cylinder at the same Re. Stability analysis of two-dimensional periodic flows around a forced-oscillating cylinder is carried out with respect to three-dimensional infinitesimal perturbations. The procedure consists of performing a Floquet type analysis of time-periodic base flows, computed using the spectral/hp element method. With the results of the Floquet calculations, considerations regarding the stability of the system are drawn, and the form of the instability at its onset is obtained. The critical Reynolds number is observed to change with the amplitude of oscillation. With respect to instabilities, unstable modes with the same symmetry as mode A of a fixed cylinder are observed; however, they present different wavelengths. Also, the instabilities observed for the oscillating cylinder are distinctively stronger in the braid shear layers. Other unstable modes similar to mode B are found. Quasi-periodic modes are observed in the 2S wake, and subharmonic mode occurrences are reported in P + S wakes. (C) 2009 Elsevier Ltd. All rights reserved.

Void fraction measurement and signal analysis from multiple-electrode impedance sensors

Void fraction sensors are important instruments not only for monitoring two-phase flow, but for furnishing an important parameter for obtaining flow map pattern and two-phase flow heat transfer coefficient as well. This work presents the experimental results obtained with the analysis of two axially spaced multiple-electrode impedance sensors tested in an upward air-water two-phase flow in a vertical tube for void fraction measurements. An electronic circuit was developed for signal generation and post-treatment of each sensor signal. By phase shifting the electrodes supplying the signal, it was possible to establish a rotating electric field sweeping across the test section. The fundamental principle of using a multiple-electrode configuration is based on reducing signal sensitivity to the non-uniform cross-section void fraction distribution problem. Static calibration curves were obtained for both sensors, and dynamic signal analyses for bubbly, slug, and turbulent churn flows were carried out. Flow parameters such as Taylor bubble velocity and length were obtained by using cross-correlation techniques. As an application of the void fraction tested, vertical flow pattern identification could be established by using the probability density function technique for void fractions ranging from 0% to nearly 70%.

Gas flow analysis in a Kraft recovery boiler

Demands for optimal boiler performance and increased concerns in lowering emission have always been the driving force in the reevaluation and evolution of the Kraft boiler: specifically the air distribution strategies that are directly related to achieving increased residence time of flue gas combustion inside the furnace which in turn lowers atmosphere emission levels and enhances boiler operation. This paper presents the results of a study that analyzes the interaction of the different multilevel air injections have on flue gas flow patterns including various quaternary air supply arrangements. Additionally, this study assesses the performance of the CFD (Computational Fluid Dynamics) model against data available in literature. Simulations were performed considering isothermal and incompressible flows, and did not take into account thermal phenomena or chemical reactions. The numerical solutions generated proved to be coherently related to the data available in literature, and provided proof of the efficiency of tertiary level air injection, as well as revealed that quaternary air injection ports arranged in a symmetrical configuration is most suitable for optimal equipment operation. (C) 2010 Elsevier B.V. All rights reserved.