VAT Based Optimization of Heat Transfer in a Flat Channel Filled With a Porous Media

2003 ◽  
Author(s):  
Ivan Catton ◽  
Kunzhong Hu
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Dissipation ◽  
Energy Transport ◽  
Heterogeneous Media ◽  
Statistical Design ◽  
Frictional Resistance ◽  
Volume Averaging ◽  
Statistical Design Of Experiments ◽  
Optimization Parameters

Developments of volume averaging theory (VAT) used to describe transport phenomena in heterogeneous media are applied to optimization of heat dissipation from a heterogeneous media. The media is a porous media representation of a pin fin heat sink (a heterogeneous layer) and the optimization process is accomplished with rigor using the idea of scaled energy transport. The problem is addressed in four steps: 1) determine the parameters needed for optimization from the two temperature VAT equations, 2) use statistical design of experiments (simulating the problem) for the many optimization parameters, 3) perform numerical simulation of the cases that are suggested through the statistical analysis of the optimization parameters, and 4) statistically analyze the numerical results to obtain an optimization response surface. The two applications are enhancement of heat transfer dissipation from a heterogeneous media while minimizing the frictional resistance and minimization of the thermal resistance (a problem of importance to all designers of heat exchangers).

Statistics of Mathematical Two-Scale Closure of Momentum, Heat and Charge Transport Problems With Stochastic Orientation of Porous Medium Capillaries

2001 ◽  
Author(s):  
V. S. Travkin ◽  
K. Hu ◽  
I. Catton
Keyword(s):  
Heat Transfer ◽  
Porous Medium ◽  
Porous Media ◽  
Volume Averaging ◽  
Governing Equations ◽  
Rigorous Approach ◽  
Flow And Heat Transfer ◽  
Model Flow ◽  
History Of ◽  
Transport Problems

Abstract The history of stochastic capillary porous media transport problem treatments almost corresponds to the history of porous media transport developments. Volume Averaging Theory (VAT), shown to be an effective and rigorous approach for study of transport (laminar and turbulent) phenomena, is used to model flow and heat transfer in capillary porous media. VAT based modeling of pore level transport in stochastic capillaries results in two sets of scale governing equations. This work shows how the two scale equations could be solved and how the results could be presented using statistical analysis. We demonstrate that stochastic orientation and diameter of the pores are incorporated in the upper scale simulation procedures. We are treating this problem with conditions of Bi for each pore is in a range when Bi ≳ 0.1 which allows even greater distinction in assessing an each additional differential, integral, or integral-differential term in the VAT equations.

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.

scholarly journals Central Composite Design in a Refinery’s Wastewater Treatment by Air Flotation

2013 ◽  
Vol 2 (3) ◽  
pp. 245-253
Keyword(s):  
Design Of Experiments ◽  
Central Composite Design ◽  
Statistical Design ◽  
Response Surfaces ◽  
Statistical Design Of Experiments ◽  
Cationic Flocculant ◽  
Optimization Parameters ◽  
Combined Action ◽  
Design Factors ◽  
Central Composite

Water resulting from the dewatering process of petroleum storage tanks was treated in a pilot separator to investigate the effectiveness of the combined action of a coagulant (aluminum sulfate) and a cationic flocculant (NALCO 71403). Central composite design of experiments was used to construct second order response surfaces for the turbidity, suspended solids and oil content as optimization parameters. The coagulant and flocculant concentrations and pH were used as design factors. The separator constructed for this purpose proved to be suitable for fast and reliable investigation of multivariable systems and for search of the optimum via statistical design of experiments.

Modeling of Forced Convection in an Electronic Device Heat Sink as Porous Media Flow

2002 ◽  
Author(s):  
Andrej Horvat ◽  
Ivan Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Sink ◽  
Electronic Device ◽  
Computer Code ◽  
Local Heat ◽  
Volume Averaging ◽  
Temperature Fields ◽  
Porous Media Flow ◽  
Transfer Coefficients

An algorithm for simulation of conjugate heat transfer used to find the most suitable geometry for an electronic chip heat sink is described. Applying Volume Averaging Theory (VAT) to a system of transport equations, a heat exchanger structure was modeled as a homogeneous porous media. The interaction between the fluid and the structure, the VAT equation closure requirement, was accomplished with drag and heat transfer coefficients, which were taken from the available literature and inserted into a computer code. The example calculations were performed for an aluminum heat sink exposed to force convection airflow. The geometry of the simulation domain and boundary conditions followed the geometry of the experimental test section. The comparison of the whole-section drag coefficient and Nusselt number as functions of Reynolds number shows a good agreement with the experimental data. The calculated temperature fields reveal the local heat flow distribution and enable further improvements of the heat sink geometry.

Exact Closure Procedures of Hierarchical VAT Capillary Thermo-Convective Problem for Turbulent and Laminar Regimes

2001 ◽  
Author(s):  
V. S. Travkin ◽  
K. Hu ◽  
I. Catton
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Turbulent Transport ◽  
Volume Averaging ◽  
Turbulent Regime ◽  
Rigorous Approach ◽  
Flow And Heat Transfer ◽  
Pore Level ◽  
Scale Properties ◽  
The Many

Abstract Volume Averaging Theory (VAT), an effective and rigorous approach for study of transport (laminar and turbulent) phenomena, is used to model flow and heat transfer in porous media. The modeling is based on a simple pore level network. The primary difficulties in applying VAT to straight capillary networks, the many unknown integral and differential terms that are needed for closure, are overcome. VAT based modeling of pore level transport in straight capillaries results in two sets of scale governing equations. One scale is the upper scale VAT equations which describe ensemble properties for flow and heat transfer in porous media. The other scale is the lower scale laminar and turbulent transport equations that represent flow and heat transport in each straight pore capillary. It is how the unknown VAT terms in the upper scale equations can be estimated using the relationships between upper scale properties and lower scale properties. Exact closures and mathematical procedures are developed for the turbulent regime, extending the previous laminar regime work. Numerical results for turbulent and laminar transport in straight capillary porous media are shown in this paper.

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.

Optimization of Absorption in a Porous Media

2004 ◽  
Author(s):  
Aleksander Vadnjal ◽  
Ivan Catton
Keyword(s):  
Porous Media ◽  
Energy Absorption ◽  
Heterogeneous Media ◽  
Maximum Level ◽  
Volume Averaging ◽  
Acoustic Energy ◽  
Heterogeneous Structure ◽  
Mathematical Basis ◽  
Optimization Task ◽  
Single Scale

A majority of past investigations focused on solutions to a specific optimization task with a very limited number of spatial parameters to be varied, usually a fixed geometric configuration, that was tuned in their search for a maximum level of acoustic energy absorption. This approach is a “single-scale” approach yielding an optimum for a certain morphology and flow intensity without giving an explanation for why it was achieved. Without an explanation, there is no guidance on how to change the design to improve its performance. For each new morphology, the experiment, whether real or numerical, needs to be performed again. In the acoustics industry there are countless research studies devoted to this problem. Travkin et al. [1] developed a mathematical basis, using volume averaging theory (VAT), see also Whitaker [2], and models for optimization of a heterogeneous, hierarchical scaled media. The treatment of the optimization process can be applied to any specific hierarchical heterostructure with the aim to optimize its performance. In this work, developments of VAT to describe transport phenomena in heterogeneous media are applied to optimization of acoustic energy absorption by a heterogeneous media. The enhancement of acoustic energy absorption is stated mathematically in a way that the lower scale viscous dissipation and the performance of the total device are incorporated for optimization. The VAT equations derived by Vadnjal and Catton [3] are the basis for a model that successfully describes the non-homogeneous nature of the porous media, allowing optimization of a heterogeneous structure for optimum performance.

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.

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