scholarly journals Applications of the Volume Averaging Theory to Momentum and Heat Transfer within Complex Flow Systems

2012 ◽  
Vol 11 (3) ◽  
pp. 1-30
Author(s):  
Akira Nakayama
Keyword(s):  
Heat Transfer ◽  
Heat Exchangers ◽  
Control Volume ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Governing Equations ◽  
Complex Flow ◽  
Flow Systems ◽  
Momentum And Heat Transfer ◽  
Volume Averaging Theory

The volume averaging theory (VAT) developed in the study of porous media is quite powerful in attacking difficult problems associate with momentum and heat transfer in complex fluid flow system, such as heat exchangers, combustors and engine nacelles. Applications of VAT to momentum and heat transfer within complex heat and flow systems are reviewed in this lecture. Such difficulties arise from geometrical complexities and conjugate heat transfer between fluids and solids. In order to overcome the difficulties, the set of the governing equations are integrated over a local control volume to obtain the macroscopic governing equations. The sub-scale (i.e. pore-scale) modeling is carried out to close the set of the equations. Subsequently, the unknown model constants are determined by conducting direct numerical simulations using a structural unit model. Various applications in heat exchangers, composting systems and human bodies are discussed to elucidate the validity of the present procedure.

scholarly journals Obtaining Closure for Fin-and-Tube Heat Exchanger Modeling Based on Volume Averaging Theory (VAT)

2011 ◽  
Vol 133 (11) ◽  
Author(s):  
Feng Zhou ◽  
Nicholas E. Hansen ◽  
David J. Geb ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Exchanger ◽  
Friction Factor ◽  
Heat Exchangers ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Length Scale ◽  
Tube Heat Exchanger ◽  
Volume Averaging Theory

Modeling a fin-and-tube heat exchanger as porous media based on volume averaging theory (VAT), specific geometry can be accounted for in such a way that the details of the original structure can be replaced by their averaged counterparts, and the VAT based governing equations can be solved for a wide range of heat exchanger designs. To complete the VAT based model, proper closure is needed, which is related to a local friction factor and a heat transfer coefficient of a representative elementary volume. The present paper describes an effort to model a fin-and-tube heat exchanger based on VAT and obtain closure for the model. Experiment data and correlations for the air side characteristics of fin-and-tube heat exchangers from the published literature were collected and rescaled using the “porous media” length scale suggested by VAT. The results were surprisingly good, collapsing all the data onto a single curve for friction factor and Nusselt number, respectively. It was shown that using the porous media length scale is very beneficial in collapsing complex data yielding simple heat transfer and friction factor correlations and that by proper scaling, closure is a function of the porous media, which further generalizes macroscale porous media equations. The current work is a step closer to our final goal, which is to develop a universal fast running computational tool for multiple-parameter optimization of heat exchangers.

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.

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.

The Use of Volume Averaging Theory (VAT) for Evaluation of Surface Heat Transfer Augmentation

2008 ◽  
Author(s):  
V. K. Tam ◽  
M. R. Chang ◽  
I. Catton
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Removal ◽  
Volume Averaging ◽  
Surface Heat ◽  
Averaging Theory ◽  
Pumping Power ◽  
Heat Transfer Augmentation ◽  
Fully Developed Turbulent Flow ◽  
Volume Averaging Theory

A model, based on Volume Averaging Theory (VAT), was developed to predict friction and heat transfer over augmented surfaces. The objective is to find augmentation that produces a higher heat removal relative to the increase in pumping power necessary to overcome the additional friction that is generated. This was accomplished with a numerical solution of the VAT transport equations for describing fully developed turbulent flow in a channel with augmented surfaces. Friction factor and Nusselt number results produced by the numerical simulation are compared with experimental data to validate the model and which of the augmented surfaces performs the best is clearly show.

Obtaining Experimental Closure for the VAT-Based Energy Equations Modeling a Heat Sink as a Porous Medium

2011 ◽  
Author(s):  
David J. Geb ◽  
Jonathan Chu ◽  
Feng Zhou ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Heat Sink ◽  
Internal Heat ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Pin Fin ◽  
Volume Averaging Theory ◽  
The Heat Transfer Coefficient

Experimentally determining internal heat transfer coefficients in porous structures has been a challenge in the design of heat exchangers. In this study, a novel combined experimental and computational method for determining the internal heat transfer coefficient within a heat sink is explored and results are obtained for air flow through basic pin fin heat sinks. These measurements along with the pressure drop allow for thermal-fluid modeling of a heat sink by closing the Volume Averaging Theory (VAT)-based governing equations, providing an avenue towards optimization. To obtain the heat transfer coefficient the solid phase is subjected to a step change in heat generation rate via induction heating, while the fluid flows through under steady state conditions. The fluid phase temperature response is measured. The heat transfer coefficient is determined by comparing the results of a numerical simulation based on volume averaging theory with the experimental results. The only information needed is the basic material properties, the flow rate, and the experimental data. The computational procedure alleviates the need for internal solid and fluid phase temperature measurements, which are difficult to make and can disturb the solid-fluid interaction. Moreover, a simple analysis allows us to proceed without knowledge of the heat generation rate, which is difficult to determine precisely. Multiple pin fin heat sink morphologies were selected for this study. Moreover, volume averaging theory scaling arguments allow a single correlation for both the heat transfer coefficient and friction factor that encompass a wide range of pin fin morphologies. It is expected that a precise tool for experimental closure of the VAT-based equations modeling a heat sink as a porous medium will allow for better modeling, and subsequent optimization, of heat sinks.

VAT Based Modeling of Plate-Pin Fin Heat Sink and Obtaining Closure From CFD Solution

2011 ◽  
Author(s):  
Feng Zhou ◽  
Nicholas Hansen ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Sink ◽  
Volume Averaging ◽  
Heat Sinks ◽  
Averaging Theory ◽  
Conservation Of Energy ◽  
Pin Fin ◽  
Fast Running ◽  
Volume Averaging Theory

A plate-pin fin heat sink (PPFHS) is composed of a plate fin heat sink (PFHS) and some pin fins planted between the flow channels. Just as the other kinds of heat sinks, it is a hierarchical multilevel device with many parameters required for its description. Volume Averaging Theory (VAT) is 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 the plate-pin fin (porous media) morphology and to describe the hierarchical nature of the heat sink. Closure for the upper level is obtained using VAT to describe the lower level. At the lower level, the media is described by a representative elementary volume (REV). Closure terms in the VAT equations are related to a local friction factor and a heat transfer coefficient of the REV. The terms in the closure expressions are complex and relating experimental data to the closure terms resulting from VAT is difficult. In this work, we model the plate-pin fin heat sink based on Volume Averaging Theory and use CFD to obtain detailed solutions of flow through an element of PPFHS and use these results to evaluate the closure terms needed for a fast running VAT based code. The VAT based code can then be used to solve the heat transfer characteristics of the higher level heat sink. The objective is to show how plate-pin fin heat sinks can be modeled as porous media based on Volume Averaging Theory and how CFD can be used in place of a detailed, often formidable, experimental effort.

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