Operating Conditions for the Hemodialysis Treatment Based on the 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.

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

Applied Thermal Engineering ◽

10.1016/j.applthermaleng.2015.01.019 ◽

2015 ◽

Vol 79 ◽

pp. 225-233 ◽

Cited By ~ 10

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

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

Journal of Heat Transfer ◽

10.1115/1.4004478 ◽

2011 ◽

Vol 133 (12) ◽

Cited By ~ 10

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.

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Genetic Algorithm Optimization of a Compact Heat Exchanger Modeled Using Volume Averaging Theory

Volume 2: Heat Transfer Enhancement for Practical Applications; Fire and Combustion; Multi-Phase Systems; Heat Transfer in Electronic Equipment; Low Temperature Heat Transfer; Computational Heat Transfer ◽

10.1115/ht2012-58067 ◽

2012 ◽

Cited By ~ 1

Author(s):

David Geb ◽

Feng Zhou ◽

George DeMoulin ◽

Ivan Catton

Keyword(s):

Genetic Algorithm ◽

Heat Exchanger ◽

Fitness Function ◽

Volume Averaging ◽

Averaging Theory ◽

Temperature Fields ◽

Tube Heat Exchanger ◽

Finned Tube Heat Exchanger ◽

Multiple Parameter ◽

Volume Averaging Theory

This paper proposes and implements a new methodology for optimizing Compact Heat Exchangers (CHXs) using a Volume Averaging Theory (VAT) model and a Genetic Algorithm (GA) optimizer. This method allows for multiple-parameter optimization of CHXs by design of their basic morphological structures, and is applied to a Finned-Tube Heat Exchanger (FTHX). A consistent model is used to describe transport phenomena in a FTHX based on VAT, which allows for the volume averaged conservation of mass, momentum, and energy equations to be solved point by point, with the morphology of the structure directly incorporated into the field equations. The equations differ from known equations and are developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in the space of every pore. These averaged equations have additional integral and differential terms that must be dealt with in order for the equation set to be closed, and recent work has provided this closure. The resulting governing equation set is relatively simple and is discretized and solved using the finite difference method. Such a computational algorithm is fast running, but still able to present a detailed picture of the temperature fields in both of the fluid flows as well as in the solid structure of the heat exchanger. A GA is integrated with the VAT-based solver to carry out the FTHX optimization, which is a ten parameter problem, and the FTHX’s effectiveness is selected as the fitness function to be optimized. This method of using the VAT-based solver fully integrated with a GA optimizer results in an all-in-one tool for performing multiple-parameter constrained optimization on FTHXs.

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