Mathematical model for coffee extraction based on the volume averaging theory

2019 ◽  
Vol 263 ◽  
pp. 1-12
Author(s):  
Yoshihiko Sano ◽  
Shun Kubota ◽  
Akito Kawarazaki ◽  
Kazuhiko Kawamura ◽  
Hajime Kashiwai ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Volume Averaging Theory

Determining the Computational Domain Length to Obtain Closure for VAT Based Modeling by 3D Numerical Simulation and Field Synergy Analysis

2010 ◽  
Author(s):  
Feng Zhou ◽  
Nicholas Hansen ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Reynolds Number ◽  
Heat Transfer Coefficient ◽  
Heat Exchanger ◽  
Transfer Coefficient ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Computational Domain ◽  
Field Synergy ◽  
Volume Averaging Theory

Volume Averaging Theory (VAT) has been used to rigorously cast the point-wise conservation of energy, momentum and mass equations into a form that represents the thermal and hydraulic properties of heat exchanger channel morphology. Closure terms in the VAT equations are related to a local friction factor and a heat transfer coefficient of the REV, which could be evaluated using scaling suggested by VAT from the output of a CFD code. To get reasonable lower scale flow field and heat transfer solutions, the length of computational domain must be determined in advance. There-dimensional numerical simulations for laminar heat transfer and fluid flow characteristics of plain finned tube heat exchangers were performed. The effects of two factors, Reynolds number and tube row number, were examined. The Reynolds number based on the fin collar outside diameter varied from 500 to 6000 and the corresponding air frontal velocity was ranged from 0.38m/s to 4.6m/s. The cases with tube row number varying from 1 to 9 were tested numerically. Field synergy principle analysis was performed for the results, including the in-depth analysis of every REV, which gave a clear perspective of the variation of heat transfer performance with the tube rows. It is found that when the number of tube row N>4, the increasing trend of the intersection angle decreases and almost keep constant when N>6, which leads to the heat transfer approaching fully developed conditions. Simulations over the computational domain with a length of 5+2+2 REVs were recommended to obtain a reasonable local flow and heat transfer field, and then the VAT based closure formulas for drag resistance coefficient and heat transfer coefficient were integrated over the sixth and seventh REV to close the heat exchanger modeling based volume averaging theory.

Buoyancy driven convection in open-cell metal foam using the volume averaging theory

2015 ◽  
Vol 79 ◽  
pp. 225-233 ◽  
Author(s):  
Sven De Schampheleire ◽  
Kathleen De Kerpel ◽  
Peter De Jaeger ◽  
Henk Huisseune ◽  
Bernd Ameel ◽  
...  
Keyword(s):  
Metal Foam ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Open Cell ◽  
Volume Averaging Theory ◽  
Buoyancy Driven Convection

scholarly journals Determination of the Number of Tube Rows to Obtain Closure for Volume Averaging Theory Based Model of Fin-and-Tube Heat Exchangers

2011 ◽  
Vol 133 (12) ◽  
Author(s):  
Feng Zhou ◽  
Nicholas E. Hansen ◽  
David J. Geb ◽  
Ivan Catton
Keyword(s):  
Heat Exchangers ◽  
Three Dimensional ◽  
Volume Averaging ◽  
Resistance Coefficient ◽  
Averaging Theory ◽  
Computational Domain ◽  
Minimum Number ◽  
Computational Fluid Dynamics Cfd ◽  
Volume Averaging Theory

Modeling of fin-and-tube heat exchangers based on the volume averaging theory (VAT) requires proper closure of the VAT based governing equations. Closure can be obtained from reasonable lower scale solutions of a computational fluid dynamics (CFD) code, which means the tube row number chosen should be large enough, so that the closure can be evaluated for a representative elementary volume (REV) that is, not affected by the entrance or recirculation at the outlet of the fin gap. To determine the number of tube rows, three-dimensional numerical simulations for plate fin-and-tube heat exchangers were performed, with the Reynolds number varying from 500 to 6000 and the number of tube rows varying from 1 to 9. A clear perspective of the variations of both overall and local fiction factor and the Nusselt number as the tube row number increases are presented. These variation trends are explained from the view point of the field synergy principle (FSP). Our investigation shows that 4 + 1 + 1 tube rows is the minimum number to get reasonable lower scale solutions. A computational domain including 5 + 2 + 2 tube rows is recommended, so that the closure formulas for drag resistance coefficient and heat transfer coefficient could be evaluated for the sixth and seventh elementary volumes to close the VAT based model.

Transport Phenomena in Heterogeneous Media: Experimental Data Reduction and Analysis

1999 ◽  
Author(s):  
V. S. Travkin ◽  
I. Catton ◽  
K. Hu ◽  
A. T. Ponomarenko ◽  
V. G. Shevchenko
Keyword(s):  
Experimental Data ◽  
Data Reduction ◽  
Heterogeneous Media ◽  
Transport Phenomena ◽  
Morphological Characteristics ◽  
Internal Heat ◽  
Volume Averaging ◽  
Scaling Parameters ◽  
The Media ◽  
Consistent Basis

Abstract Volume averaging theory (VAT) is used to bring a consistent basis to experimental data reduction and analysis by examples in several areas of transport phenomena. Many common correlations, and their weaknesses, are examined using a unified scaling procedure that allows them to be compared to one another. Momentum resistance and internal heat transfer dependencies are analyzed and compared. VAT based analysis is shown to reveal the influence of morphological characteristics of the media, to suggest scaling parameters that allow a wide variety of different porous media morphologies to be normalized, often eliminating the need for further experimental efforts, and to clarify the relationships between differing experimental configurations. The origin, and insufficiency, of electrical conductivity and momentum transport “cross-correlation” approaches in efforts to find analogies by mathematical comparison without examining the physical foundations of phenomena are described and explained.

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