Modeling Transient Churn-Annular Flows in a Long Vertical Pipe

2013 ◽  
Author(s):  
M. V. C. Alves ◽  
J. R. Barbosa ◽  
P. J. Waltrich ◽  
G. Falcone
Keyword(s):  
Annular Flow ◽  
Large Scale ◽  
Coefficient Matrix ◽  
Vertical Tube ◽  
Flow Conditions ◽  
Vertical Pipe ◽  
One Dimensional ◽  
The One ◽  
Energy Equations ◽  
Liquid Flows

A mathematical model is presented to describe the behavior of transient gas-liquid flows involving the churn and annular flow patterns in a long vertical tube. The HyTAF (Hyperbolic Transient Annular Flow) code, developed specifically for this study, is based on the one-dimensional multi-fluid formulation and takes account of hydrodynamic non-equilibrium flow conditions by means of relationships for the rates of droplet entrainment and deposition. A finite difference algorithm is employed to solve the hyperbolic system of mass, momentum and energy equations via the Split Coefficient Matrix Method. The modeling results are compared with experimental data for steady-state annular and churn flows obtained from the literature and with pressure and flow rate induced transient churn-annular flow data generated in a large scale facility (48-mm ID, 42-m long test section).

Sensitivity Analysis of the Wall Shear Model to the Correlations for Frequency and Slug Holdup in the Gas-Liquid Slug Flow in Pipes

2015 ◽  
Vol 1104 ◽  
pp. 61-67
Author(s):  
Luiz Eduardo Melo Lima ◽  
Eugênio Spanó Rosa
Keyword(s):  
Sensitivity Analysis ◽  
Mixture Model ◽  
Liquid Mixture ◽  
Shear Model ◽  
One Dimensional ◽  
Intermittent Behavior ◽  
Wall Shear ◽  
The One ◽  
Isothermal Gas ◽  
Liquid Flows

The one-dimensional mixture model efficiently predicts gas-liquid flows dominated by gravity force. The advantages of the mixture model are the absence of interfacial terms and the reduced number of transport equations, but its weakness lies on the constitutive laws to predict the wall shear force of a gas-liquid mixture. The objective of this work is to realize a sensitivity analysis of the wall shear model (based on the intermittent behavior of the gas and liquid structures) to the correlations for frequency and slug holdup in the one-dimensional, steady state mixture model applied to an isothermal gas-liquid mixture flowing in the slug regime. The numerical results for the pressure gradient obtained here are compared against experimental data from previous work.

High Pressure Diesel Engine Modeling

2003 ◽  
Author(s):  
Riccardo Baudille ◽  
Gino Bella ◽  
Rossella Rotondi
Keyword(s):  
Liquid Fuel ◽  
Initial Conditions ◽  
Injection Velocity ◽  
Dimensional Model ◽  
Flow Conditions ◽  
One Dimensional ◽  
Engine Modeling ◽  
Fuel Jet ◽  
Initial Drop ◽  
The One

In multi hole Diesel injectors, cavitation can offer advantages in the development on the fuel spray, because the primary atomization of the liquid fuel jet can be improved due to the enhanced turbulence. Several multi dimensional models of cavitating nozzle flow have been developed in order to provide information about the flow at the exit of a cavitating orifice. In this paper an analytical one-dimensional model, by Sarre et al. [1], to predict the flow conditions at the exit of a cavitating nozzle, is analyzed. The results obtained are compared with the ones obtained using the multi dimensional code Fluent in order to investigate the predictive capability of the one-dimensional code. The model provides initial conditions for multidimensional spray modeling: the effective injection velocity and the initial drop or injected liquid ‘blob’ size. The simulations were performed using an improved version of the KIVA3V code, in which an hybrid break up model, developed by the authors, is used and the results in terms of penetrations and global SMD are compared with the experimental ones. The one dimensional model predicts reasonable discharge coefficient for sharp injector geometry. Where the r/d ratio increases and the cavitation effects appear not clearly marked there are same discrepancies between the one dimensional and the multidimensional approach.

Impact of the wastegate opening on radial turbine performance under steady and pulsating flow conditions

2019 ◽  
Vol 234 (2-3) ◽  
pp. 652-668 ◽  
Author(s):  
Ahmed Ketata ◽  
Zied Driss ◽  
Mohamed Salah Abid
Keyword(s):  
Mass Flow ◽  
Large Deviation ◽  
Pulse Frequency ◽  
Pulsating Flow ◽  
Flow Conditions ◽  
One Dimensional ◽  
Loop Area ◽  
Modeling Methodology ◽  
Turbine Performance ◽  
The One

The present article attempts to describe the behavior of wastegated turbines under various steady and pulsating flow conditions. For this, meanline and one-dimensional numerical codes including appropriate modeling approaches for wastegated turbines have been developed with the FORTRAN language. These codes were validated against experiments with an established test rig at the National School of Engineers of Sfax. The discharge coefficient map of the wastegate was determined with a developed correlation built from experiments, and it was served as an input to the developed codes for interpolations during computation. This correlation is based on a two-dimensional non-linear dose-response fitting relationship instead of classical polynomial function which is one novelty of the article in addition to the one-dimensional modeling methodology. The normalized root mean square error (NRMSE) of both cycle-averaged efficiency and mass flow parameter (MFP) remains below 2% which confirms the validity of the proposed calculation approach. The results indicated a large deviation in the turbine performance under pulsating flow conditions compared to the steady state ones. The shape of the hysteresis loop of the turbine efficiency remains unchanged toward the variation of the wastegate valve angle at the same pulse frequency. The mass flow hystereses loop area is decreased by around 50% as the pulse frequency increases from 33 up to 133.33 Hz. An increase of less than 1% of the cycle-averaged efficiency has been reported when the bypass flow through the wastegate increases. The fluctuation of the efficiency is decreased by 1.5% when the wastegate valve becomes fully opened under the whole range of the pulse frequency.

Water Quality Control of the Andelse Maas Basin, The Netherlands, by Iron Dosing

1985 ◽  
Vol 17 (4-5) ◽  
pp. 769-780 ◽  
Author(s):  
A. C. Hoekstra ◽  
K. D. Maiwald
Keyword(s):  
Chlorophyll A ◽  
Algal Growth ◽  
Phosphate Removal ◽  
Advection Equation ◽  
Flow Conditions ◽  
Water Quality Control ◽  
One Dimensional ◽  
The Hague ◽  
The One ◽  
High Phosphate

The Dune Water Works of The Hague pumps yearly about 45 million cubic meters of water from the Andelse Maas Basin to the dunes for infiltration purposes. The water in the Andelse Haas Basin is strongly influenced by the Meuse river. Phosphate concentrations are so high that algal growth causes difficulties in filters and dunes. For phosphate reduction purposes, iron is dosed into the basin. Several limnological variables are monitored based on weekly measurements. A mathematical model has been developed for the description of the eutrophication in the basin. The model is time and space dependent and based on the one-dimensional dispersion-advection equation. Two separate submodels are used, one for the simulation of flow conditions and one for the algae and nutrient kinetics. The ortho-phosphate reduction is modelled as a first order process. The eutrophication model has been calibrated, verified and used for a prediction of chlorophyll-a and ortho-phosphate concentrations for the case of the shut down of the iron dosing installation. The dosing of iron appears to be a very effective way for phosphate removal. Termination of the dosing would give unacceptable high phosphate and chlorophyll-a concentrations. Present investigations are focussed upon the minimization of the amount of iron dosing.

The Mexico Earthquake of September 19, 1985—A Theoretical Investigation of Large- and Small-scale Amplification Effects in the Mexico City Valley

1988 ◽  
Vol 4 (3) ◽  
pp. 609-633 ◽  
Author(s):  
P-Y. Bard ◽  
M. Campillo ◽  
F. J. Chávez-Garcia ◽  
F. Sánchez-Sesma
Keyword(s):  
Mexico City ◽  
Large Scale ◽  
Small Scale ◽  
Clay Layer ◽  
Local Surface ◽  
One Dimensional ◽  
Mexico Earthquake ◽  
The One ◽  
Deep Sediments ◽  
Lateral Heterogeneities

The linear, large-scale and small-scale amplification effects in the Mexico City valley, related to both the surficial clay layer and the underlying thick sediments, are investigated with two-dimensional (2D) models and compared with the results of simple one-dimensional (1D) models. The deep sediments are shown to be responsible, on their own, for an amplification ranging between 3 and 7, a part of which is due to the 2D effects in case of low damping and velocity gradient. This result is consistent with the observed relative amplification around 0.5 Hz at CU stations with respect to TACY station. The amplification due to the clay layer is much larger (above 10), and the corresponding 2D effects have very peculiar characteristics. On the one hand, the local surface waves generated on any lateral heterogeneity exhibit a strong spatial decay, even in case of low damping (2%), and the motion at a given site is therefore affected only by lateral heterogeneities lying within a radius smaller than 1 km. On the other hand, these local 2D effects may be extremely large, either on the very edges of the lake-bed zone, or over localized thicker areas, where they induce a duration increase and an overamplification. The main engineering consequences of these results are twofold: i) microzoning studies in Mexico City should take into account the effects of deep sediments, and ii) as the surface motion in the lake-bed zone is extremely sensitive to local heterogeneities, 1D models are probably inappropriate in many parts of Mexico City.

scholarly journals Insights from Single-File Diffusion into Cooperativity in Higher Dimensions

2016 ◽  
Vol 11 (01) ◽  
pp. 9-38 ◽  
Author(s):  
Takeshi Ooshida ◽  
Susumu Goto ◽  
Takeshi Matsumoto ◽  
Michio Otsuki
Keyword(s):  
Large Scale ◽  
Mean Square Displacement ◽  
Colloidal Suspensions ◽  
Higher Dimensions ◽  
Colloidal Systems ◽  
One Dimensional ◽  
Single File ◽  
The Mean ◽  
The One ◽  
Single File Diffusion

Diffusion in colloidal suspensions can be very slow due to the cage effect, which confines each particle within a short radius on one hand, and involves large-scale cooperative motions on the other. In search of insight into this cooperativity, here the authors develop a formalism to calculate the displacement correlation in colloidal systems, mainly in the two-dimensional (2D) case. To clarify the idea for it, studies are reviewed on cooperativity among the particles in the one-dimensional (1D) case, i.e. the single-file diffusion (SFD). As an improvement over the celebrated formula by Alexander and Pincus on the mean-square displacement (MSD) in SFD, it is shown that the displacement correlation in SFD can be calculated from Lagrangian correlation of the particle interval in the one-dimensional case, and also that the formula can be extended to higher dimensions. The improved formula becomes exact for large systems. By combining the formula with a nonlinear theory for correlation, a correction to the asymptotic law for the MSD in SFD is obtained. In the 2D case, the linear theory gives description of vortical cooperative motion.

Subsonic Adiabatic Flow in a Duct of Constant Cross-Sectional Area

1964 ◽  
Vol 68 (638) ◽  
pp. 117-126 ◽  
Author(s):  
A. J. Ward Smith
Keyword(s):  
Flow Theory ◽  
Flow Conditions ◽  
Mean Flow ◽  
Flow Properties ◽  
Cross Sectional ◽  
Fully Developed Flow ◽  
One Dimensional ◽  
Dimensional Flow ◽  
Loss Coefficients ◽  
The One

SummaryStarting from the momentum integral equation an analysis is made of fully-developed flow in a straight pipe. This analysis shows the assumptions implicit in the one-dimensional theory of adiabatic constant-area flow with friction. For conditions of practical interest the approximations associated with the use of the one-dimensional flow theory are shown to be small.Flow with a developing velocity profile and flow in a bend are then analysed. Introducing approximations revealed in the analysis of fully-developed flow, a simple relation is obtained between the variation of mean flow properties along the duct under incompressible and compressible flow conditions. This relation may be written in the same form as the corresponding relation derived using the one-dimensional flow theory. In a similar manner to one-dimensional flow theory, the relation is readily extended to apply over a series of components of constant cross-sectional area.The results of the analysis are also presented in terms of static and total pressure loss coefficients. This form of presentation demonstrates that there are appreciable effects of Mach number, on the pressure loss coefficients, where they are often assumed to be small.The analysis does not enable the variation of the mean flow properties to be calculated ab initio. Its application is to be found in problems where a knowledge of the performance of a component, or series of components, is required under compressible flow conditions, the performance under incompressible flow conditions already being available from theoretical or experimental data.A comparison of predicted and experimental data for flow in bends and flow in combinations of duct components shows good agreement over much of the subsonic speed regime.

Key Stages of the Formation of AlPO4-11 via Crystallization of Aluminophosphate Gel Prepared with Boehmite

2018 ◽  
Vol 18 (6) ◽  
pp. 6-13
Author(s):  
M. R. Agliullin ◽  
Z. R. Khairullina ◽  
A. V. Faizullin ◽  
A. I. Petrov ◽  
A. A. Badretdinova ◽  
...  
Keyword(s):  
Molecular Sieves ◽  
Large Scale ◽  
Intermediate Phase ◽  
Strong Acid ◽  
One Dimensional ◽  
Stage Crystallization ◽  
Acid Centers ◽  
The One ◽  
Adsorption Desorption ◽  
First Time

The one-dimensional channel pore system and the moderately strong acid centers inherent in aluminophosphate (AlPO4-11) and silicoaluminophosphate (SAPO-11) molecular sieves make them promising catalyst for hydroisomerization of higher n-paraffins. However, the mechanism of crystallization of these materials is not well understood as yet. XRD,27Al and31P MAS NMR, lowtemperature adsorption-desorption of nitrogen, and SEM techniques were used for the first time for studying the stage crystallization of aluminophosphate AlPO4-11 for commercial boehmite based aluminium source. AlPO4-11 was shown to form via an intermediate phase based on layered crystalline aluminophosphate. It was established that highly crystalline and phase-pure AlPO4-11 was formed at 200 °C during 6 to 24 hours. When the crystallization at 200 °C lasted for more than two days, AlPO4-11 turned into non-porous cristobalite. The results obtained will be used for developing methods for deliberate control of the phase composition and crystallinity of industrially important silicoaluminophosphate sieves SAPO-11 with required properties to develop promising catalysts based thereon for large-scale processes of hydroisomerization of n-paraffins.

Rapid spin up and spin down of flow along slopes

2021 ◽  
Keyword(s):  
Large Scale ◽  
Ekman Transport ◽  
Return Flow ◽  
Extended Model ◽  
Dimensional Model ◽  
Unified Framework ◽  
One Dimensional ◽  
Ocean Ridges ◽  
Slope Flow ◽  
The One

Abstract The near-bottom mixing that allows abyssal waters to upwell tilts isopycnals and spins up flow over the flanks of mid-ocean ridges. Meso- and large-scale currents along sloping topography are subjected to a delicate balance of Ekman arrest and spin down. These two seemingly disparate oceanographic phenomena share a common theory, which is based on a one-dimensional model of rotating, stratified flow over a sloping, insulated boundary. This commonly used model, however, lacks rapid adjustment of interior flows, limiting its ability to capture the full physics of spin up and spin down of along-slope flow. Motivated by two-dimensional dynamics, the present work extends the one-dimensional model by constraining the vertically integrated cross-slope transport and allowing for a barotropic cross-slope pressure gradient. This produces a closed secondary circulation by forcing Ekman transport in the bottom boundary layer to return in the interior. The extended model can thus capture Ekman spin up and spin down physics: the interior return flow is turned by the Coriolis acceleration, leading to rapid rather than slow diffusive adjustment of the along-slope flow. This transport-constrained one-dimensional model accurately describes twodimensional mixing-generated spin up over an idealized ridge and provides a unified framework for understanding the relative importance of Ekman arrest and spin down of flow along a slope.

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