David Geb

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

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 multipleparameter optimization of heat exchangers. [DOI: 10.1115/1.4004393]

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

Modelling of fin-and-tube heat exchangers based on Volume Averaging Theory (VAT) requires proper closure of the VAT based governing equations. Closure can be obtained from reasonable lower scale solutions of a 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 re-circulation 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 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.

Internal Heat Transfer Coefficient Determination in a Packed Bed From the Transient Response Due to Solid Phase Induction Heating

Non-intrusive measurements of the internal heat transfer coefficient in the core of a randomly packed bed of uniform spherical particles are made. Under steady, one-dimensional flow the spherical particles are subjected to a step change in volumetric heat generation rate via induction heating. The fluid temperature response is measured. The internal heat transfer coefficient is determined by comparing the results of a numerical simulation based on volume averaging theory (VAT) with the experimental results. The only information needed is the basic material and geometric properties, the flow rate, and the fluid temperature response data. The computational procedure alleviates the need for solid and fluid phase temperature measurements within the porous medium. The internal heat transfer coefficient is determined in the core of a packed bed, and expressed in terms of the Nusselt number, over a Reynolds number range of 20 - 500. The Nusselt number and Reynolds number are based on the VAT scale hydraulic diameter, . The results compare favorably to those of other researchers and are seen to be independent of particle diameter. The success of this method, in determining the internal heat transfer coefficient in the core of a randomly packed bed of uniform spheres, suggests that it can be used to determine the internal heat transfer coefficient in other porous media.

Nonlocal Modeling and Swarm-Based Design of Heat Sinks

Cooling electronic chips to satisfy the ever-increasing heat transfer demands of the electronics industry is a perpetual challenge. One approach to addressing this is through improving the heat rejection ability of air-cooled heat sinks, and nonlocal thermal-fluid-solid modeling based on volume averaging theory (VAT) has allowed for significant strides in this effort. A number of optimization methods for heat sink designers who model heat sinks with VAT can be envisioned due to VATs singular ability to rapidly provide solutions, when compared to computational fluid dynamics (CFD) approaches. The particle swarm optimization (PSO) method appears to be an attractive multiparameter heat transfer device optimization tool; however, it has received very little attention in this field compared to its older population-based optimizer cousin, the genetic algorithm (GA). The PSO method is employed here to optimize smooth and scale-roughened straight-fin heat sinks modeled with VAT by minimizing heat sink thermal resistance for a specified pumping power. A new numerical design tool incorporates the PSO method with a VAT-based heat sink solver. Optimal designs are obtained with this new tool for both types of heat sinks, the performances of the heat sink types are compared, the performance of the PSO method is discussed with reference to the GA method, and it is observed that this new method yields optimal designs much quicker than traditional approaches. This study demonstrates, for the first time, the effectiveness of combining a VAT-based nonlocal thermal-fluid-solid model with population-based optimization methods, such as PSO, to design heat sinks for electronics cooling applications. The VAT-based nonlocal modeling method provides heat sink design capabilities, in terms of solution speed and model rigor, that existing modeling methods do not match.

Genetic Algorithm Optimization of a Compact Heat Exchanger Modeled Using 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.Copyright

Internal Transport Coefficient Measurements in Random Fiber Matrix Heat Exchangers

Experimental determination of transport coefficients, in particular internal heat transfer coefficients, in heterogeneous and hierarchical heat transfer devices such as compact regenerative heat exchangers has posed a persistent challenge for designers. The goal of this study is to (1) present a new general treatment of the experimental determination of such design data, to (2) provide simple correlations for high porosity random fiber matrices for broad design applications, and to (3) illustrate how such measurements close the formidable integro-differential volume averaging theory (VAT) equations governing transport phenomena in porous media. The combined experimental and computational method employed here for determining the internal heat transfer coefficient in the porous structure is based on the VAT model and combines with simple pressure drop measurements to yield the relevant design data for eight different high porosity random fiber samples. The design data are correlated based on a porous media length scale derived from the VAT model governing equations and the transport coefficient correlations obtained are valid for gas flows over a Reynolds number range between 5 and 70. Finally, the correlations are related to explicit, rigorously derived, lower-scale expressions arising from the VAT model. With the illustration of a new experimental tool, and the production of new simple design correlations for high porosity random fiber matrices for regenerative heat transfer applications, within the context of the hierarchical VAT model, future VAT-based simulation studies of such devices may be pursued. Moreover, the nonlocal modeling provided by VAT paves the way to meaningful optimization studies due to its singular ability to provide rigorous modeling and fast numerical solutions for transport phenomena in regenerative compact heat exchangers

Genetic Algorithm Optimization of a Finned-Tube Heat Exchanger Modeled With Volume-Averaging Theory

This paper proposes and implements a new methodology for optimizing finned-tube heat exchangers (FTHEs) using a volume-averaging theory (VAT) hierarchical physical model and a genetic algorithm (GA) numerical optimizer. This method allows for multipleparameter constrained optimization of FTHEs by design of their basic morphological structures. A consistent model is used to describe transport phenomena in a FTHE 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 and full conjugate effects included. The equations differ from those often presented in porous media modeling and are developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in every pore space. 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 for FTHEs. The resulting governing equation set is relatively simple and is discretized and quickly solved numerically. Such a computational solution 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 FTHE numerical optimization, which is a ten parameter problem, and the FTHE is optimized subject to imposed constraints. This method of using the VAT-based solver fully integrated with a GA optimizer results in a new all-inone tool for performing multiple-parameter constrained optimization on FTHEs. [DOI: 10.1115/1.4024091]

Volume Averaging Theory (VAT) based modeling and closure evaluation of scale-roughened plane fin heat sink

The present paper describes an effort to model a plane fin heat sink (PFHS) with scale-roughened surfaces based on Volume Averaging Theory (VAT) and evaluate the closure terms of the model using CFD code. Modeling a PFHS 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 solved for a wide range of heat sink 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 (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 code to obtain detailed solutions of flow and heat transfer through an element of the scale-roughened heat sink 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 sink. The objective is to show how 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 to close the VAT based model.

Numerical Investigation on Air Side Performance of Fin-and-Tube Heat Exchangers With Large Diameter Tubes and Large Number of Tube Rows

In the present study, air-side turbulent heat transfer and friction characteristics of fin-and-tube heat exchangers with a large number of tube rows and large diameter of tubes are investigated numerically. Finite Volume Method based CFD software, Ansys CFX, was used as the 3-D Reynolds-averaged Navier-Stokes Solver. A k-ω based Shear-Stress-Transport (SST) model was used to predict the turbulent flow and heat transfer through the fin-and-tube heat exchanger coil. The effects of parameters such as Reynolds number, the number of tube rows, tube diameter, tube pitches and fin pitch are examined. In the end, correlations for the Nusselt number and friction factor which applicable to fin-and-tube heat exchangers with large number of large-diameter tube rows are proposed.Copyright

Modeling of Pin Fin Heat Sinks Based on Volume Averaging Theory

In this paper, a consistant model is developed to describe transport phenomena in a pin fin heat sink that take into account the scales and other characteristics of the medium morphology. The specific geometry of the heat sink is accounted for in such a way that the details of the original structure are replaced by their averaged counterparts. Equation sets allowing for turbulence and two-temperature or two-concentration diffusion are obtained for non-isotropic porous media with interface exchange. The equations differ from known equations and were developed using a rigorous averaging technique, hierarchical modeling methodology, and fully turbulent models with Reynolds stresses and fluxes in the space of every pore. The transport equations are shown to have additional integral and differential terms. These terms are closed experimentally from available data for pin fin morphology. The resulting equation set is relatively simple and is descretized using the finite difference method. Such computational algorithm is fast running, but still able to present a detailed picture of themperature fields in the airflow as well as in the solid structure of the heat sink. The calculated friction factor and thermal resistance are compared with experimental data to verify the porous model and validate the numerical code. The results calculated by the code agrees with the experimental data quite well, which offers possibility for multiple parameter optimization using Design of Experiment (DOE) to achieve high cooling capabilities.Copyright