Scale-up Technique of Slurry Pipelines—Part 1: Turbulence Modeling

1986 ◽  
Vol 108 (4) ◽  
pp. 269-277 ◽  
Author(s):  
M. C. Roco ◽  
S. Mahadevan
Keyword(s):  
Kinetic Energy ◽  
Finite Volume ◽  
Solid Wall ◽  
Mathematical Formulation ◽  
Specific Interaction ◽  
Scale Up ◽  
Three Dimensions ◽  
Semiempirical Methods ◽  
Time Averaging ◽  
Two Phase

A kinetic energy turbulence model is proposed for the flow simulation and scale-up of slurry pipelines (in Part 1). The numerical integration is performed by using a modified finite volume technique with application to high convective, two-phase flows, in two and three dimensions (in Part 2 [1]). The mixture kinetic energy and eddy viscosity one-equation turbulence models are compared. The constitutive equations and model constants are tested using laboratory experiments and then employed for large-scale applications. The governing equations are derived from the space/time averaging of the momentum equations and integrated in the pipe cross section using the finite volume approach. The specific interaction stresses (liquid-liquid, liquid-solid, solid-solid and solid-wall) are expressed in the mathematical formulation. The predictions for the velocity and concentration distributions, as well as on the mean velocity-headloss correlations, have been compared to available experimental data (water-sand, water-glass, water-coal mixtures; of concentrations αS = 5 – 40 vol percent, in pipes of various diameters D = 40 – 500 mm). The suggested model can simulate multi-species particulate pipe flow for which the semiempirical methods cannot be satisfactorily applied. The numerical tests and comparison to experiments show the model capabilities to scale-up data from laboratory to real flow situations via infinitesimal two-phase flow analysis.

Scale-up Technique of Slurry Pipelines—Part 2: Numerical Integration

1986 ◽  
Vol 108 (4) ◽  
pp. 278-285
Author(s):  
M. C. Roco ◽  
S. Mahadevan
Keyword(s):  
Kinetic Energy ◽  
Numerical Integration ◽  
Finite Volume ◽  
Turbulence Model ◽  
Eddy Viscosity ◽  
Scale Up ◽  
Transport Equations ◽  
Convective Transport ◽  
Two Phase Flows ◽  
Two Phase

A kinetic energy turbulence model has been proposed for the computer flow simulation and scale-up of slurry pipelines (in Part 1 [1]). The numerical integration is performed by using a modified finite volume technique, with application to high-convective two-phase flows in two and three dimensions (in Part 2). The mixture kinetic energy and eddy viscosity turbulence models are compared. The one-equation eddy-viscosity turbulence model (εt - model) is formulated in Part 2 and applied for the multi-species particle slurry flow in cylindrical pipes. A modified finite volume technique is proposed for high convective transport equations, for one and two-phase flows. The integral formulation per volume yields surface and volume integrals, that are stored and counted only by interfaces using a multidimensional approach. The nonlinear distributions in volumes and on interfaces are approximated employing the derivatives in the normal and tangent directions to the bounding surfaces. Linear, analytical (upwind) and logarithmic laws of interpolations are considered for internal flows. The numerical approach was tested with good results for transport equations of momentum and various contaminants (solid particles, temperature, eddy-viscosity) in pipes. Experimental data for one and two-phase flows are compared to the integral finite volume predictions. The proposed finite volume technique can economically simulate complex flow situations encountered in the slurry pipeline scale-up applications.

A comparison of finite volume method and sharp model for two dimensional saltwater intrusion modeling

2014 ◽  
Vol 41 (3) ◽  
pp. 191-196 ◽  
Author(s):  
Boutaina Bouzouf ◽  
Zhi Chen
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Saltwater Intrusion ◽  
Mathematical Formulation ◽  
Test Case ◽  
Two Phase ◽  
Closed Form Solutions ◽  
Analytical Test ◽  
Mathematical Equations ◽  
Volume Method

Seawater intrusion in coastal aquifers is a 3-D phenomenon. However, 3-D regional aquifer models are often limited by insufficient geological and hydrological data, the large horizontal to vertical scales ratio, and by numerical constraints. A mathematical formulation and numerical implementation of the model for saltwater intrusion problems are presented in this paper. The mathematical model is based on assumption of two-phase flow between saltwater and freshwater and Dupuit approximation. Finite volume method is used as the numerical method in non-structured grids to have flexibility upon complex configuration domain and was compared to sharp model that uses finite difference method. Both models are based on the same governing mathematical equations. Finite volume method was validated using analytical test case studies with known closed form solutions, and the results showed good agreement. Both models have then been applied to the case of saltwater intrusion into a real study case. The comparison between both methods indicates that the finite volume method provides predictions closer to the observed results.

Solid Phase Contribution in the Two-Phase Turbulence Kinetic Energy Equation

1990 ◽  
Vol 112 (3) ◽  
pp. 351-361 ◽  
Author(s):  
T. W. Abou-Arab ◽  
M. C. Roco
Keyword(s):  
Kinetic Energy ◽  
Energy Equation ◽  
Solid Phase ◽  
Density Ratio ◽  
Turbulence Kinetic Energy ◽  
Time Averaging ◽  
Two Phase ◽  
Carrier Fluid ◽  
Double Time ◽  
Energy Equations

This paper presents a multiphase turbulence closure employing one transport equation, namely, the turbulence kinetic energy equation. The proposed form of this equation is different from the earlier formulations in some aspects. The power spectrum of the carrier fluid is divided into two regions, which interact in different ways and at different rates with the suspended particles as a function of the particle-eddy size ratio and density ratio. The length scale is described algebraically. A double-time averaging approach for the momentum and kinetic energy equations is adopted. The resulting turbulence correlations are modeled under less restrictive assumptions comparative to the previous work. The closures for the momentum and kinetic energy equations are given. Comparisons of the predictions with experimental results on liquid-solid jet and gas-solid pipe flow show satisfactory agreement.

scholarly journals Longitudinal change in left ventricular 4D flow kinetic energy after myocardial infarction

2021 ◽  
Vol 22 (Supplement_1) ◽  
Author(s):  
H Ben-Arzi ◽  
A Das ◽  
C Kelly ◽  
RJ Van Der Geest ◽  
A Chowdhary ◽  
...  
Keyword(s):  
Myocardial Infarction ◽  
Kinetic Energy ◽  
Left Ventricular ◽  
Three Dimensions ◽  
Longitudinal Change ◽  
P Value ◽  
4D Flow ◽  
Longitudinal Changes ◽  
Funding Sources ◽  
End Diastolic Volume

Abstract Funding Acknowledgements Type of funding sources: Foundation. Main funding source(s): British Heart Foundation HRUK Background. Four-dimensional flow (4D flow) cardiovascular magnetic resonance (CMR) imaging provides quantification of intra-cavity left ventricular (LV) flow kinetic energy (KE) parameters in three dimensions. Myocardial infarction (MI) is known to cause acute alterations in intra-cardiac blood flow but assessments of longitudinal changes are lacking. Purpose. Assess longitudinal changes in LV flow post ST-elevation myocardial infarction (STEMI). Method. Twenty acutely reperfused STEMI patients (13 men, 7 women, mean age 54 ± 9 years) underwent 3T CMR acutely (within 5-7 days) and 3 months post-MI.  CMR protocol included functional imaging, late gadolinium enhancement and 4D flow. Using Q-MASS, LV KE parameters were derived and indexed to LV end-diastolic volume (LVKEiEDV). Based on acute ejection fraction (EF), patients were grouped as follows: preserved (pEF) EF >50%, reduced (rEF) EF <50% including mild (rEF= 40-49%), moderate to severe (EF <40%) impairment.  Results. Out of 20 patients, 13 had rEF acutely (7 mild rEF, 6 moderate to severe rEF). Acute LVKEiEDV parameters varied significantly between pEF and rEF (Table). At 3 months, pEF and mild rEF patients showed a significant (P < 0.05) reduction in average, systolic and peak-A wave LVKEiEDV. Mild rEF patients also had significant (P < 0.05) reduction in minimal and peak-E wave LVKEiEDV. However in patients with moderate to severe rEF in the acute scan, there were no significant change by 3 months (Figure). Conclusion. Following MI, 4D flow LVKE derived biomarkers significantly decreased over time in pEF and mild rEF groups but not in moderate to severe rEF group. 4D flow assessment might provide incremental prognostic value beyond EF assessment alone. Table pEF (n = 7) rEF (n = 13) V1 V2 P-value V1 V2 P-value EF(%) 56 ± 5 55 ± 4 0.40 41 ± 7 47 ± 9 0.01 Infarct Size(%) 31 ± 20 15 ± 9 0.04 18 ± 13† 16 ± 11 0.41 LV KEiEDV parameters Average(µJ/ml) 9 ± 2 7 ± 2 0.02 10 ± 3† 8 ± 3 0.01 Minimal(µJ/ml) 1 ± 0.6 1 ± 0.5 0.46 1.3 ± 0.5 1 ± 0.6 0.03 Systolic(µJ/ml) 10 ± 4 7 ± 2 <0.01 12 ± 4† 7 ± 3 <0.01 Diastolic(µJ/ml) 8 ± 3 7 ± 2 0.13 9 ± 3 8 ± 3 0.09 Peak-E wave(µJ/ml) 22 ± 9 23 ± 8 0.44 20 ± 7 18 ± 10 0.23 Peak-A wave(µJ/ml) 18 ± 10 11 ± 4 0.04 17 ± 9 14 ± 7 0.02 †P < 0.05 V1 comparison between pEF and rEF Abstract Figure

The effect of effectuation and causation approach on entrepreneurial orientation in the presence of leader dominance and self-efficacy

2022 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ma Jun ◽  
Fitri Rini Ariyesti ◽  
Sumran Ali ◽  
Peng Xiaobao
Keyword(s):  
Entrepreneurial Orientation ◽  
Self Efficacy ◽  
Scale Up ◽  
Chief Executive ◽  
Three Dimensions ◽  
Chinese Firms ◽  
Strategic Manoeuvring ◽  
Firm Level ◽  
Content Type ◽  
Leader Traits

Purpose Entrepreneurial orientation (EO) has witnessed a daunting rise in firm-level practices; to some extent, it has been augmented by the factors such as globalization and technological shift. The wide variety of literature has explained the importance of EO for firm performance. However, it has not yet been explored at a firm-level the approaches of causation and effectuation through the prism of leader traits such as leader dominance and self-efficacy as administrative ability and EO as strategic manoeuvring with strategic decisions obliged as a spin of firms. Design/methodology/approach The authors used the quantitative method to analyse the proposed relationships. For this reason, the authors targeted the Chinese firms to collect the data through the semi-structured survey from December 2020 to March 2021 and contributed to the literature by investigating 480 valid responses of leaders from Chinese firms. Findings The findings support the incorporated view of causation and effectuation on EO, which serve as vital strategic manoeuvring along with leader traits for firm stability and growth. Practical implications This study assists the decision-makers (including the top management team, Chief Financial Officer and Chief Executive Officer choose the particular approach (effectual or causal) to create the new venture/new product/new process or scale up the existing firm on another level for optimal benefits by considering their existing resources. Originality/value EO is a unidirectional process with three dimensions: innovativeness, proactiveness and risk-taking that could directly favour the firm by considering the well-known approaches (effectuation and causation) in crisis circumstances (like Covid-19). These approaches help the executives enhance their firm’s performance and maintain its sustainability and stability in crisis conditions by effectively using the available resources within its boundaries.

scholarly journals An adaptive finite-volume method for a model of two-phase pedestrian flow

2011 ◽  
Vol 6 (3) ◽  
pp. 401-423 ◽  
Author(s):  
Stefan Berres ◽  
◽  
Ricardo Ruiz-Baier ◽  
Hartmut Schwandt ◽  
Elmer M. Tory ◽  
...  
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Pedestrian Flow ◽  
Two Phase ◽  
Volume Method
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