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.

Hierarchical Modeling and Closure Evaluation for Fin-and-Tube Heat Exchangers Using 3-D Numerical Simulation

2012 ◽  
Author(s):  
Feng Zhou ◽  
David Geb ◽  
George DeMoulin ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Exchanger ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Cfd Modeling ◽  
Original Structure ◽  
Tube Heat Exchanger ◽  
Wide Range ◽  
Volume Averaging Theory

A plain fin-and-tube heat exchanger was modeled based on Volume Averaging Theory (VAT) and the closure for the model was evaluated using CFD. Modeling a fin-and-tube heat exchanger as porous media based on 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 efficiently solved for a wide range of parameters. 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 (REV). The terms in the closure expressions are complex and sometimes relating experimental data to the closure terms is difficult. In this work we use CFD to obtain detailed solutions of flow and heat transfer through an element of a fin-and-tube heat exchanger and use these results to evaluate the closure terms needed for a fast running VAT based code, which can then be used to solve the heat transfer characteristics of a higher level heat exchanger. The objective is to show how heat sinks can be modeled as a porous media based on Volume Averaging Theory and how CFD can be used in place of a detailed, often formidable, experimental effort to obtain closure for a VAT based model.

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.

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

2012 ◽  
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.

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.

Obtaining Closure for Heat Exchanger Modeling Based on Volume Averaging Theory (VAT)

2010 ◽  
Author(s):  
Feng Zhou ◽  
Nicholas Hansen ◽  
Ivan Catton
Keyword(s):  
Heat Exchanger ◽  
Hydraulic Properties ◽  
Volume Averaging ◽  
Finned Tube ◽  
Averaging Theory ◽  
Conservation Of Energy ◽  
Tube Heat Exchanger ◽  
Finned Tube Heat Exchanger ◽  
The Media ◽  
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. 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 are evaluated using scaling suggested by VAT from either experimental data or the output of a CFD code. The VAT equations for a finned tube heat exchanger are given and that the key parameters can be obtained by suitable scaling is demonstrated.

VAT Based Modeling of Heat Exchanger and Obtaining Closure From CFD Solution

2010 ◽  
Author(s):  
Feng Zhou ◽  
Nicholas Hansen ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Experimental Data ◽  
Heat Exchanger ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Conservation Of Energy ◽  
Fast Running ◽  
The Media ◽  
Flow Through ◽  
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 heat exchanger channel morphology. 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 Volume Averaging Theory (VAT) is difficult. In this work we use CFD to obtain detailed solutions to flow through an element of a heat exchanger 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 exchanger. A comparison is then made of the CFD closure and experimental data rescaled by VAT scaling. The objective is to show how heat exchangers 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.

Design Optimization of a Shell and Tube Heat Exchanger Using Volume Averaging Theory

2021 ◽  
Author(s):  
Akshay Bharadwaj Krishna ◽  
Timothy Fisher ◽  
Ivan Catton ◽  
Portonovo Ayyaswamy
Keyword(s):  
Heat Exchanger ◽  
Design Optimization ◽  
Volume Averaging ◽  
Averaging Theory ◽  
Tube Heat Exchanger ◽  
Shell And Tube ◽  
Volume Averaging Theory

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.

Heat Transfer Performance of Different Nanofluids Flows in a Helically Coiled Heat Exchanger

2013 ◽  
Vol 832 ◽  
pp. 160-165 ◽  
Author(s):  
Mohammad Alam Khairul ◽  
Rahman Saidur ◽  
Altab Hossain ◽  
Mohammad Abdul Alim ◽  
Islam Mohammed Mahbubul
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Heat Exchanger ◽  
Pressure Drop ◽  
Transfer Coefficient ◽  
Friction Factor ◽  
Heat Exchangers ◽  
Heat Transfer Performance ◽  
Volume Concentration ◽  
Transfer Performance

Helically coiled heat exchangers are globally used in various industrial applications for their high heat transfer performance and compact size. Nanofluids can provide excellent thermal performance of this type of heat exchangers. In the present study, the effect of different nanofluids on the heat transfer performance in a helically coiled heat exchanger is examined. Four different types of nanofluids CuO/water, Al2O3/water, SiO2/water, and ZnO/water with volume fractions 1 vol.% to 4 vol.% was used throughout this analysis and volume flow rate was remained constant at 3 LPM. Results show that the heat transfer coefficient is high for higher particle volume concentration of CuO/water, Al2O3/water and ZnO/water nanofluids, while the values of the friction factor and pressure drop significantly increase with the increase of nanoparticle volume concentration. On the contrary, low heat transfer coefficient was found in higher concentration of SiO2/water nanofluids. The highest enhancement of heat transfer coefficient and lowest friction factor occurred for CuO/water nanofluids among the four nanofluids. However, highest friction factor and lowest heat transfer coefficient were found for SiO2/water nanofluids. The results reveal that, CuO/water nanofluids indicate significant heat transfer performance for helically coiled heat exchanger systems though this nanofluids exhibits higher pressure drop.

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