scholarly journals CFD Modeling of Slurry Flows in Horizontal Pipes

2008 ◽  
Author(s):  
Franz H. Herna´ndez ◽  
Armando J. Blanco ◽  
Luis Rojas-Solo´rzano
Keyword(s):  
Experimental Data ◽  
Numerical Solutions ◽  
Solid Phase ◽  
Flow Behavior ◽  
Flow Regimes ◽  
Computational Domain ◽  
Physical Scale ◽  
Wide Range ◽  
Slurry Flows ◽  
Eulerian Models

Liquid-solid two-phase flows are found in numerous operations in the chemical, petroleum, pharmaceutical and many other industries. In numerous cases, the mixture or slurry that flows is composed by a suspension of solid particles (dispersed phase) transported by a liquid (continuum phase). However, the large number and range of variables encountered in slurry flows, in the case of pipelines, cause the flow behavior of these slurry systems to vary over a wide range of conditions, and consequently, different approaches have been used to describe the behavior of different flow regimes. Therefore, there are numerous studies of particular cases that cover limited ranges of conditions. In consequence, the experimental approach is necessarily limited by geometric and physical scale factors. For these reasons, Computational Fluid Dynamics, CFD, constitutes an ideal technique for predicting the general flow behavior of these systems. CFD models in this area can be divided in two different classes: Eulerian-Eulerian and Lagrangian-Eulerian models. Differences between these models are related to the way the solid phase flow is represented. Lagrangian-Eulerian models calculate the path and motion of each particle, while Eulerian-Eulerian models treat the particle phase as a continuum and average out motion on the scale of individual particles. This work focuses on the Eulerian-Eulerian approach for modeling the flow of a mixture of sand particles and water in a horizontal pipe. Homogeneous and heterogeneous flow regimes are considered. The k-ε model was used for modeling turbulent effects. Additionally, closure of solid-phase momentum equations requires a description for the solid-phase stress. Constitutive relations for the solid-phase stress considering the inelastic nature of particle collisions based on the Gas Kinetic Theory concepts have been used. Governing equations are solved numerically using the control volume-based finite element method. An unstructured non-uniform grid was chosen to discretize the entire computational domain. A second-order scheme in space and time was used. Numerical solutions in fully developed turbulent flow were found. Results show that flow predictions are very sensitive to the restitution coefficient and pseudo-viscosity of the solid phase. The mean pressure gradients from numerical solutions were compared with results obtained using the correlations of Einstein, Thomas and Krieger for homogeneous cases and with experimental data found in the open literature for heterogeneous cases. The solutions were found to be in good agreement with both correlations and experimental data. In addition, these numerical results were closer to experimental data than results obtained using other numerical models.

Eulerian-Eulerian Modeling of Non-Newtonian Slurries Flow in Horizontal Pipes

2009 ◽  
Author(s):  
Boris M. Bossio ◽  
Armando J. Blanco ◽  
Franz H. Herna´ndez
Keyword(s):  
Experimental Data ◽  
Base Fluid ◽  
Solid Phase ◽  
Flow Behavior ◽  
Turbulent Viscosity ◽  
Pressure Gradients ◽  
Wide Range ◽  
Slurry Flows ◽  
Mean Pressure ◽  
Eulerian Models

Slurries transport through circular pipelines is present in many industries: oil, mineral, water and others. There are many variables involved in slurry flows, causing the flow behavior of these slurry systems to vary over a wide range, and therefore, different approaches have been used to describe their behavior in various flow regimes. At some typical applications, the rheology of the base fluid is itself non-Newtonian. Due to the wide range of variables and their variations, the experimental approach is necessarily limited by geometric and physical scale factors. For a non-Newtonian base fluid, only some particular cases that cover a limited range of conditions have been reported. For these reasons, numerical simulation constitutes an ideal technique for predicting the general flow behavior of these systems. Models in this area can be divided in two different classes: Eulerian-Eulerian and Lagrangian-Eulerian. Lagrangian-Eulerian models calculate the path and motion of each particle, while Eulerian-Eulerian models treat the particle phase as a continuum and average out motion on the scale of individual particles. This work focuses on the Eulerian-Eulerian approach for modeling the flow of a mixture of sand particles and a non-Newtonian fluid in a horizontal pipe. The steady-state rheological behavior of the base fluid was expressed by the three-parameter Sisko model. Homogeneous and heterogeneous flow regimes are considered. For the present study, the widely used “k-ε model” is employed to model turbulent viscosity. The k-ε turbulence model introduces two additional variables: the kinetic energy of the fluid turbulence, k, and the dissipation rate of this kinetic energy, ε. These two variables are solved throughout the fluid domain via two additional differential transport equations. The k-ε model is therefore commonly referred to as a “two-equation” turbulence model. The turbulent viscosity is then determined as a function of k and ε. Additionally, closure of solid-phase momentum equations requires a description for the solid-phase stress. Constitutive relations for the solid-phase stress, considering the inelastic nature of particle collisions based on kinetic theory concepts, have been used. Governing equations were solved numerically using the control volume-based finite element method. An unstructured non-uniform grid was chosen to cover the entire computational domain. A second-order scheme in space was used. Precise numerical solutions in a fully developed turbulent flow were found. Flow behavior for different sand concentrations was simulated. Results for the mean pressure gradients were compared with experimental data. The results turned out to be in compliance with those from the experimental data, for a sand concentration of less than 5%. Numerical simulations of non-Newtonian slurry flows provide a method that can relate properties of the fluid and solid component of the slurry, and does not entail the time and expenses needed for empirical studies. This also might provide a further sight to develop correlations between mean pressure gradients and slurry mean velocity.

Correlations Between Pressure Drop and Two-Phase Flow Regimes in Microchannel Networks

2009 ◽  
Author(s):  
Christian Weinmu¨ller ◽  
Dimos Poulikakos
Keyword(s):  
Experimental Data ◽  
Pressure Drop ◽  
Flow Regime ◽  
Single Phase ◽  
Two Phase Flow ◽  
Flow Regimes ◽  
Phase Flow ◽  
Two Phase ◽  
Research Activities ◽  
Wide Range

Microfluidics has experienced a significant increase in research activities in recent years with a wide range of applications emerging, such as micro heat exchangers, energy conversion devices, microreactors, lab-on-chip devices and micro total chemical analysis systems (μTAS). Efforts to enhance or extend the performance of single phase microfluidic devices are met by two-phase flow systems [1, 2]. Essential for the design and control of microfluidic systems is the understanding of the fluid/hydrodynamic behavior, especially pressure drop correlations. These are well established for single phase flow, however, analytical correlations for two-phase flow only reflect experimentally obtained values within an accuracy of ± 50% [3, 4]. The present study illustrates the effect of two-phase flow regimes on the pressure drop. Experimental measurement data is put into relation of calculated values based on established correlations of Lockhart-Martinelli with Chisholm modifications for macroscopic flows [5, 6] and Mishima-Hibiki modifications for microscale flows [7]. Further, the experimental pressure drop data is superimposed onto two-phase flow maps to identify apparent correlations of pressure drop abnormalities and flow regimes. The experiments were conducted in a square microchannel with a width of 200 μm. Optical access is guaranteed by an anodically bonded glass plate on a MEMS fabricated silicon chip. Superficial velocities range from 0.01 m/s to 1 m/s for the gas flow and from 0.0001 m/s to 1 m/s for the liquid flow with water as liquid feed and CO2 as gas. The analysis of the flow regimes was performed by imaging the distinct flow regimes by laser induced fluorescence microscopy, employing Rhodamine B as the photosensitive dye. The pressure drop was synchronically recorded with a 200 mbar, 2.5 bar and 25 bar differential pressure transmitter and the data was exported via a LabView based software environment, see Figure 1. Figure 2 illustrates the experimentally obtained pressure drop in comparison to the calculated values based on the Lockhard-Martinelli correlation with the Chisholm modification and the Mishima-Hibiki modification. For both cases the predications underestimate the two-phase pressure drop by more than 50%. Nevertheless, the regression of the experimental data has an offset of linear nature. Two-phase flow is assigned to flow regime maps of bubbly, wedging, slug or annular flow defined by superficial gas and liquid velocities. In Figure 3 the pressure drop is plotted as a surface over the corresponding flow regime map. Transition lines indicate a change of flow regimes enclosing an area of an anticline in the pressure data. In the direct comparison between the calculated and the measured values, the two surfaces show a distinct deviation. Especially, the anticline of the experimental data is not explained by the analytical correlations. Figure 4 depicts the findings of Figure 3 at a constant superficial velocity of 0.0232 m/s. The dominant influence of the flow regimes on the pressure drop becomes apparent, especially in the wedging flow regime. The evident deviation of two-phase flow correlations for the pressure drop is based on omitting the influence of the flow regimes. In conclusion, the study reveals a strong divergence of pressure drop measurements in microscale two-phase flow from established correlations of Lockhart-Martinelli and recognized modifications. In reference to [8, 9], an analytical model incorporating the flow regimes and, hence, predicting the precise pressure drop would be of great benefit for hydrodynamic considerations in microfluidics.

A Model for Flow Distribution in Manifolds

1971 ◽  
Vol 93 (1) ◽  
pp. 7-12 ◽  
Author(s):  
R. A. Bajura
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Analytical Model ◽  
Distribution Systems ◽  
Numerical Solutions ◽  
Flow Behavior ◽  
Flow Distribution ◽  
Analytical Investigation ◽  
Momentum Balance ◽  
Distribution Equation

An analytical investigation of the performance of flow distribution systems was conducted for both intake and exhaust manifolds. Primary emphasis was placed on configurations in which the lateral tubes formed sharp-edged junctions at right angles to the manifold axis. A mathematical model describing the flow behavior at a discreet branch point was formulated in terms of a momentum balance along the manifold. The model was extended to the case of continuous discharge or intake for a uniformly porous manifold. Numerical solutions of the governing flow distribution equation were obtained and compared with experimental data. Dimensionless parameters characterizing the performance of manifolds were formulated from the analytical model.

Laminar spread of a circular liquid jet impinging axially on a rotating disc

2019 ◽  
Vol 864 ◽  
pp. 449-489 ◽  
Author(s):  
B. Scheichl ◽  
A. Kluwick
Keyword(s):  
Numerical Solutions ◽  
Film Flow ◽  
Thin Liquid Film ◽  
Jet Impingement ◽  
Flow Regimes ◽  
Careful Analysis ◽  
Rotating Disc ◽  
Viscous Shear ◽  
Wide Range ◽  
The Impact

The steady laminar annular spread of a thin liquid film generated by a circular jet which impinges perpendicularly in direction of gravity on the centre of a rotating disc is examined both analytically and numerically. Matched asymptotic expansions of the flow quantities provide the proper means for studying the individual flow regimes arising due to the largeness of the Reynolds number formed with the radius of the jet, its slenderness and the relative magnitude of the centrifugal body force. This is measured by a suitably defined Rossby number, $Ro$. The careful analysis of jet impingement predicts a marked influence of gravity and surface tension on the film flow, considered in the spirit of a shallow-water approach, only through the vorticity imposed by the jet flow. Accordingly, associated downstream conditions are disregarded as the local Froude and Weber numbers are taken to be sufficiently large. Hence, the parabolic problem shaped from the governing equations in a rigorous manner describes the strongly supercritical spread of a developed viscous film past an infinite disc, essentially controlled by $Ro$. Its numerical solutions are discussed for a wide range of values of $Ro$. The different flow regimes reflecting varying effects of viscous shear and centrifugal force are elucidated systematically to clarify the surprising richness of flow phenomena. Special attention is paid to the cases $Ro\gg 1$ and $Ro\ll 1$. The latter, referring to relatively high disc spin, implies a delicate breakdown of the asymptotic flow structure, thus requiring a specific analytical and numerical treatment. Finally, the impact of gravity and capillarity and thus of the disc edge on the film flow is envisaged in brief.

scholarly journals Undesirable Flow Behavior in a Proposed Validation Data Set

2010 ◽  
Author(s):  
Richard W. Johnson ◽  
Hugh M. McIlroy ◽  
Ryan C. Johnson ◽  
Daniel P. Christensen
Keyword(s):  
Experimental Data ◽  
Recirculation Zone ◽  
Flow Behavior ◽  
National Laboratory ◽  
Index Of Refraction ◽  
Department Of Energy ◽  
Computational Domain ◽  
Scaled Model ◽  
Validation Data ◽  
Data Set

The next generation nuclear plant (NGNP), whose development is supported by the U. S. Department of Energy, will be a very high temperature reactor (VHTR). The VHTR is a single-phase helium-cooled reactor that will provide helium at up to 800 °C. The prospect of a coolant at these temperatures circulating in the reactor vessel demands that careful analysis be performed to ensure that excessively hot spots are not created and that sufficient mixing of the coolant is obtained. Computational fluid dynamics (CFD) coupled with heat transfer will be used to perform the desired analyses. However, primarily because of the imperfect nature of modeling turbulent flow, any CFD calculations used to perform nuclear reactor safety analysis must be validated against experimental data. Experimental data have been taken in a scaled section of the lower plenum of a prismatic VHTR at the matched index of refraction (MIR) facility at the Idaho National Laboratory. These data were taken with the intent that they be examined for use as validation data. A series of investigations have been conducted to assess the MIR data. Issues that have already been examined include the extent of the required computational domain, the outlet boundary condition, the inlet data and the effect of the turbulence model. One of the jets that flow into the model impacts on a wedge, which represents a portion of a hexagonal graphite block that is part of the inner wall of the lower plenum. The nature of the flow below this particular jet is such that a randomly varying recirculation zone is created. This recirculation zone is seen to change in size, causing a relatively long-time scale of motion or disturbance on the flow downstream. It is concluded that such a feature is undesirable in a validation data set, firstly because of its apparent random nature and, secondly, because to obtain an appropriate longtime average would be impractical because of the compute time required. It is found that by eliminating the first of the four inlet jets into the scaled model, the resulting recirculation zone is rendered stable.

scholarly journals Robust Mode Analysis

Mathematics ◽  
2021 ◽  
Vol 9 (9) ◽  
pp. 1057
Author(s):  
Gemunu H. Gunaratne ◽  
Sukesh Roy
Keyword(s):  
Experimental Data ◽  
Bluff Body ◽  
Numerical Solutions ◽  
Dynamic Mode Decomposition ◽  
Mode Analysis ◽  
Jet Flows ◽  
Dynamic Mode ◽  
Reacting Flow ◽  
Model Free ◽  
Wide Range

In this paper, we introduce a model-free algorithm, robust mode analysis (RMA), to extract primary constituents in a fluid or reacting flow directly from high-frequency, high-resolution experimental data. It is expected to be particularly useful in studying strongly driven flows, where nonlinearities can induce chaotic and irregular dynamics. The lack of precise governing equations and the absence of symmetries or other simplifying constraints in realistic configurations preclude the derivation of analytical solutions for these systems; the presence of flow structures over a wide range of scales handicaps finding their numerical solutions. Thus, the need for direct analysis of experimental data is reinforced. RMA is predicated on the assumption that primary flow constituents are common in multiple, nominally identical realizations of an experiment. Their search relies on the identification of common dynamic modes in the experiments, the commonality established via proximity of the eigenvalues and eigenfunctions. Robust flow constituents are then constructed by combining common dynamic modes that flow at the same rate. We illustrate RMA using reacting flows behind a symmetric bluff body. Two robust constituents, whose signatures resemble symmetric and von Karman vortex shedding, are identified. It is shown how RMA can be implemented via extended dynamic mode decomposition in flow configurations interrogated with a small number of time-series. This approach may prove useful in analyzing changes in flow patterns in engines and propulsion systems equipped with sturdy arrays of pressure transducers or thermocouples. Finally, an analysis of high Reynolds number jet flows suggests that tests of statistical characterizations in turbulent flows may best be done using non-robust components of the flow.

Prediction of Ingress Through Turbine Rim Seals: Part 2—Combined Ingress

2010 ◽  
Author(s):  
J. Michael Owen ◽  
Oliver Pountney ◽  
Gary Lock
Keyword(s):  
Experimental Data ◽  
Rotational Speed ◽  
Numerical Solutions ◽  
External Flow ◽  
Operating Conditions ◽  
Flow Rates ◽  
Wide Range ◽  
Experimental Values ◽  
The One ◽  
Empirical Constants

In Part1 of this two-part paper, the orifice equations were solved for the case of externally-induced ingress, where the effects of rotational speed are negligible. In Part 2, the equations are solved, analytically and numerically, for combined ingress (CI) where the effects of both rotational speed and external flow are significant. For the CI case, the orifice model requires the calculation of three empirical constants, including Cd,e,RI and Cd,e,EI, the discharge coefficients for rotationally-induced (RI) and externally-induced (EI) ingress. For the analytical solutions, the external distribution of pressure is approximated by a linear saw-tooth model; for the numerical solutions, a fit to the measured pressures is used. It is shown that, although the values of the empirical constants depend on the shape of the pressure distribution used in the model, the theoretical variation of Cw,min (the minimum nondimensional sealing flow rate needed to prevent ingress) depends principally on the magnitude of the peak-to-trough pressure difference in the external annulus. The solutions of the orifice model for Cw,min are compared with published measurements, which were made over a wide range of rotational speeds and external flow rates. As predicted by the model, the experimental values of Cw,min could be collapsed onto a single curve, which connects the asymptotes for RI and EI ingress at the respective smaller and larger external flow rates. At the smaller flow rates, the experimental data exhibit a minimum value of Cw,min, which undershoots the RI asymptote. Using an empirical correlation for Cd,e, the model is able to predict this undershoot, albeit smaller in magnitude than the one exhibited by the experimental data. The limit of the EI asymptote is quantified, and it is suggested how the orifice model could be used to extrapolate effectiveness data obtained from an experimental rig to engine-operating conditions.

Prediction of Flow Stress for Superplastic Tension Deformation

2014 ◽  
Vol 941-944 ◽  
pp. 1501-1504
Author(s):  
Zhi Ping Guan ◽  
Ming Wen Ren ◽  
Pin Kui Ma ◽  
Po Zhao
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Flow Behavior ◽  
High Accuracy ◽  
Superplastic Flow ◽  
Al Alloy ◽  
Strain Rates ◽  
Good Reliability ◽  
Wide Range

With the development of numerical calculation and precision forming, constitutive equations are required to possess high accuracy and good reliability, rather than simplicity of mathematical form. Due to simple algorithm and constant parameters, the conventional constitutive models can not be suited to describing superplastic flow behavior which represents complex responses with a large strain. In this study, through surface fitting on experimental data from tension tests performed over a wide range of strain rates, tensile velocities and loads, an empirical approach was proposed to establish constitutive equation for complex superplastic behavior of Zn-5%Al alloy at 340 °C. The empirical constitutive equation not only represents the strain dependence and the strain rate dependence of stress, but also reflects the coupling effects of strain and strain rate on stress, which can not be achieved by traditional models. A comparison between the predicted flow stresses and the experimental data verified that the empirical constitutive equation has high accuracy and good reliability on modeling superplastic flow behavior of Zn-5%Al alloy at 340 °C in a wide range of strains 0~2.5 and strain rates 7.0×10-5~8.0×10-2s-1.

Constitutive Modeling for Superplastic Flow Behavior of H62 Alloy

2014 ◽  
Vol 941-944 ◽  
pp. 1488-1491
Author(s):  
Zhi Ping Guan ◽  
Hong Jie Jia ◽  
Ming Wen Ren ◽  
Dong Lai Wei
Keyword(s):  
Experimental Data ◽  
Constitutive Equation ◽  
Strain Rate ◽  
Flow Behavior ◽  
Constant Strain Rate ◽  
Superplastic Flow ◽  
Strain Rates ◽  
Good Ability ◽  
Wide Range ◽  
Comprehensive Reliability

In order to precisely describe superplastic flow behavior of H62 alloy, a empirical constitutive equation was established based on the experimental data, which were obtained from the constant strain rate tensions (2.0×10-4~4.0×10-2s-1) at 720 °C. Through verification of the constitutive equation with the experimental data in constant strain rate tensions and constant velocity tensions, it was indicated that the empirical constitutive equation has high accuracy and comprehensive reliability in a wide range of strain rates (2.0×10-4~2.0×10-2s-1) and strains (0~1.8). In addition, the empirical constitutive equation has a good ability to model the superplastic flow behavior of H62 alloy at 720 °C under other deformation conditions besides constant strain rate tension.

Prediction of Ingress Through Turbine Rim Seals—Part II: Combined Ingress

2011 ◽  
Vol 134 (3) ◽  
Author(s):  
J. Michael Owen ◽  
Oliver Pountney ◽  
Gary Lock
Keyword(s):  
Experimental Data ◽  
Rotational Speed ◽  
Numerical Solutions ◽  
External Flow ◽  
Operating Conditions ◽  
Flow Rates ◽  
Wide Range ◽  
Experimental Values ◽  
The One ◽  
Empirical Constants

In Part I of this two-part paper, the orifice equations were solved for the case of externally induced (EI) ingress, where the effects of rotational speed are negligible. In Part II, the equations are solved, analytically and numerically, for combined ingress (CI), where the effects of both rotational speed and external flow are significant. For the CI case, the orifice model requires the calculation of three empirical constants, including Cd,e,RI and Cd,e,EI, the discharge coefficients for rotationally induced (RI) and EI ingress. For the analytical solutions, the external distribution of pressure is approximated by a linear saw-tooth model; for the numerical solutions, a fit to the measured pressures is used. It is shown that although the values of the empirical constants depend on the shape of the pressure distribution used in the model, the theoretical variation of Cw,min (the minimum nondimensional sealing flow rate needed to prevent ingress) depends principally on the magnitude of the peak-to-trough pressure difference in the external annulus. The solutions of the orifice model for Cw,min are compared with published measurements, which were made over a wide range of rotational speeds and external flow rates. As predicted by the model, the experimental values of Cw,min could be collapsed onto a single curve, which connects the asymptotes for RI and EI ingress at the respective smaller and larger external flow rates. At the smaller flow rates, the experimental data exhibit a minimum value of Cw,min, which undershoots the RI asymptote. Using an empirical correlation for Cd,e, the model is able to predict this undershoot, albeit smaller in magnitude than the one exhibited by the experimental data. The limit of the EI asymptote is quantified, and it is suggested how the orifice model could be used to extrapolate the effectiveness data obtained from an experimental rig to engine-operating conditions.

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