Single and Multiresponse Adaptive Design of Experiments with Application to Design Optimization of Novel Heat Exchangers

Engineering design optimization often involves complex computer simulations. Optimization with such simulation models can be time consuming and sometimes computationally intractable. In order to reduce the computational burden, the use of approximation-assisted optimization is proposed in the literature. Approximation involves two phases, first is the Design of Experiments (DOE) phase, in which sample points in the input space are chosen. These sample points are then used in a second phase to develop a simplified model termed as a metamodel, which is computationally efficient and can reasonably represent the behavior of the simulation response. The DOE phase is very crucial to the success of approximation assisted optimization. This dissertation proposes a new adaptive method for single and multiresponse DOE for approximation along with an approximation-based framework for multilevel performance evaluation and design optimization of air-cooled heat exchangers. The dissertation is divided into three research thrusts. The first thrust presents a new adaptive DOE method for single response deterministic computer simulations, also called SFCVT. For SFCVT, the problem of adaptive DOE is posed as a bi-objective optimization problem. The two objectives in this problem, i.e., a cross validation error criterion and a space-filling criterion, are chosen based on the notion that the DOE method has to make a tradeoff between allocating new sample points in regions that are multi-modal and have sensitive response versus allocating sample points in regions that are sparsely sampled. In the second research thrust, a new approach for multiresponse adaptive DOE is developed (i.e., MSFCVT). Here the approach from the first thrust is extended with the notion that the tradeoff should also consider all responses. SFCVT is compared with three other methods from the literature (i.e., maximum entropy design, maximin scaled distance, and accumulative error). It was found that the SFCVT method leads to better performing metamodels for majority of the test problems. The MSFCVT method is also compared with two adaptive DOE methods from the literature and is shown to yield better metamodels, resulting in fewer function calls. In the third research thrust, an approximation-based framework is developed for the performance evaluation and design optimization of novel heat exchangers. There are two parts to this research thrust. First, is a new multi-level performance evaluation method for air-cooled heat exchangers in which conventional 3D Computational Fluid Dynamics (CFD) simulation is replaced with a 2D CFD simulation coupled with an e-NTU based heat exchanger model. In the second part, the methods developed in research thrusts 1 and 2 are used for design optimization of heat exchangers. The optimal solutions from the methods in this thrust have 44% less volume and utilize 61% less material when compared to the current state of the art microchannel heat exchangers. Compared to 3D CFD, the overall computational savings is greater than 95%

A Review of State of the Art in Modeling of Air-to-Refrigerant Heat Exchangers for HVAC&R Applications

Air-to-refrigerant heat exchangers are a key component in all air-conditioning, heat pump and refrigeration systems. The most common of types of air-to-refrigerant heat exchangers are tube-fin and microchannel heat exchangers. There has always been a great emphasis on understating the underlying physics and improving the performance of these heat exchangers. More recently, researchers have been investigating the use of small hydraulic diameter flow channels as well as novel heat transfer surfaces for use in such heat exchangers. The novel designs not only include shape optimized tubes, but also tube bundles with varying tube and fin geometries. In order to design optimum heat exchangers for a given application, it is crucial to use a reliable thermal-hydraulic model to evaluate the performance of air-to-refrigerant heat exchangers. In the last two decades, significant strides have been made in modeling of tube-fin and microchannel heat exchangers. The different modeling techniques include the use of performance maps, LMTD and epsilon-NTU based methods and fully discretized finite volume approaches. In terms of accuracy, the finite volume models are by far the preferred ones. The goal of this paper is to present the state of the art in finite volume modeling of air-to-refrigerant heat exchangers and to highlight research that stretches the boundaries of conventional heat exchanger modeling methods. Â The review starts out with a comprehensive survey of finite volume models in the literature and their capabilities to account for the various underlying physical phenomenon. High level modeling paradigms are derived and the best practices are highlighted. The various methods of geometry and circuitry representation and solution methodologies are summarized. Majority of these models rely on empirical correlations for local heat transfer and pressure drop evaluations. The use of such correlations has its own challenges and the lessons learned from the literature in this context are highlighted. Air and refrigerant flow maldistribution, especially in microchannel heat exchangers, is a critical phenomenon that needs to be accounted for in such models. Refrigerant flow maldistribution models in the literature range from user-specified quality and mass flow distribution profiles to more sophisticated methods that use CFD-based co-simulation techniques. The different techniques for handling dehumidifying conditions, such as those in an evaporator, are summarized. Finite volume models can be computationally expensive, especially when used as a part of a system simulation. The different methods used to speed up individual HX simulations are reviewed. Lastly, recent literature on optimization of air-to-refrigerant heat exchangers is presented. The review concludes with some thoughts on what the future of air-to-refrigerant heat exchanger design and optimization might be

Enhanced Integer Permutation based Genetic Algorithm for Optimization of Tube-Fin Heat Exchanger Circuitry with Splits and Merges

Tube-fin heat exchangers (HXs) are widely used in air-conditioning and heat pump applications. The performance of these heat exchangers is strongly influenced by the refrigerant circuitry. Studies have proved that by optimizing the refrigerant circuitry, the performance of HXs can be significantly improved. In our previous research, an Integer Permutation based Genetic Algorithm (IPGA) was developed to obtain the optimal circuitry designs. Our previous research showed that IPGA demonstrates superior capability to obtain better refrigerant circuitries with lower computational cost than the other methods in literature. And the optimal circuitry designs obtained from IPGA are manufacturable with the available tooling. However, the IPGA developed previously cannot generate designs with splitting and merging of circuits. To remedy this limitation, a new chromosome which can represent circuitry with splitting and merging of circuits is developed. In addition to the six genetic operators implemented previously, two new genetic operators are developed to generate splits and merges. As a result, the enhanced IPGA can explore the solution space more thoroughly than the previous IPGA. A case study using an evaporator from an A-type indoor unit shows that, given the similar capacity improvements obtained from the enhanced IPGA compared with the previous IPGA, the refrigerant pressure drop reduction obtained from the enhanced IPGA is 26.5% compared against 1.0% pressure drop reduction from the previous IPGA. The benchmark of the enhanced IPGA with other methods in literature demonstrates that the enhanced IPGA can generate circuitry designs with performance superior to those obtained from other methods

Standardized Polynomials for Fast Evaluation of Refrigerant Thermophysical Properties

Steady state and dynamic simulation and optimization are a key step in the design of heating, ventilation, air-conditioning and refrigeration (HVAC&R) systems. It is well known that the computation time in such simulations is dominated by the refrigerant thermophysical property calculations. These calculations generally involve calculating all thermophysical properties given one or two independent parameters. Refrigerant thermophysical properties are typically calculated using some fundamental equations of state (EOS). The NIST REFPROP database is an industrially accepted standard for EOS implementation. Due to the iterative nature of the EOS calculations in REFPROP, the computation time is significant and sometimes not acceptable for optimization of HVAC&R systems. In this paper, a comprehensive approach for speeding up thermophysical property calculations is presented, including the functional forms as well as the implementation aspects. A set of polynomial functional forms are presented that allow for approximation of all the thermophysical properties in all the regions for a particular refrigerant (pure fluid or a blend) of interest. The polynomials can be easily scaled to make a judicious trade-off between computation time and accuracy. Analyses for refrigerants such as R1234yf, R32, R410A, R407C and R407F are presented. Using the proposed curve fits, the saturation properties for any refrigerant can be evaluated using less than 42 floating point operations (flops) and the flash calculations with less than 300 flops per property. The mean absolute error in predicted saturation properties is 0.001% and that of flash calculations is within 0.05%. Overall the individual property calculations are 100-5000 times faster than NIST REFPROP resulting in component and system simulation speed up factor of more than 100 for refrigerant blends. The use of two standardized and scalable functional forms for approximating all properties for all refrigerants of interest facilitates easy and robust implementation on a variety of steady state and transient simulation platforms as well as on hardware since limited data needs to be stored

A Comprehensive Evaluation of Regression Uncertainty and the Effect of Sample Size on the AHRI-540 Method of Compressor Performance Representation

AHRI-540 is the current standard defining the methods for representing compressor performance data. While this standard is widely used across the industry, multiple factors contribute to inaccuracies in data representation including measurement uncertainty, regression uncertainty, compressor to compressor variation, and operation outside of the normal operating envelope (extrapolation). In addition, the number and location of points in the operating envelop also affects the accuracy of the resulting 10-coefficient polynomial. The measurement uncertainty is well known and can be factored into the data reduction. However, the measurement uncertainty is generally not propagated into the regression uncertainty and hence the overall uncertainty in prediction using the polynomial is not known. This uncertainty also changes according to the number of samples used for developing the polynomial. Â As a first step of the evaluation, a regression uncertainty analysis was conducted using a Monte Carlo simulation method. Results showed that the average uncertainty in mass flow rate prediction can be as high as 4% and that in power prediction can be as high as 5%. The worst case maximum absolute error in predicted mass flow rate across all data sets was 17% and that for power was 9%. Error in predicted power and mass flow rate is higher for larger capacity compressors. For most compressors, the high errors occur in the region of the envelope with low suction and low discharge dew point temperatures. Â A study of sampling considering different sample sizes and multiple sampling methods was conducted. Two additional methods of compressor performance representation were also analyzed. This analysis was presented with several challenges, particularly since the compressor operating envelope is a non-rectangular domain. A sampling method using Latin Hypercube Design (LHS) and a proposed alternative sampling method based on polygonal design of experiments (PDOE) were evaluated. The resulting models were validated against a measured data set of more than 600 points encompassing the operating envelope for each compressor. In general, both the LHS and PDOE methods yielded similar errors in mass flow rate for samples sizes of 12, 14 and 16. Thus, for mass flow rate, it is possible to build a model with 12 systematically selected test points. For power prediction, the average error for the LHS and PDOE methods using AHRI540 and two other methods was lower than 2% for all sample sizes

Airside Performance Correlations and Optimal Heat Pump Heat Exchanger Designs Based on 0.5mm-2mm Finless Round Tube Bundles

The use of small diameter tubes in air-to-refrigerant heat exchangers has significant advantages, which include increase in heat transfer coefficient, reduction in size, reduction in material or weight and reduction in refrigerant charge. However, there are no air-side correlations for small diameter tubes below 2mm in the literature. Furthermore, conventional empirical correlation development relies on testing of samples, which is inherently time consuming, expensive and has a limited range of applicability. This paper presents equations for airside friction and heat transfer characteristics for bare tube air-to-refrigerant Heat eXchangers (HX) with tube diameters ranging from 0.5mm to 2mm, and are valid for 2 to 40 rows of tubes in both staggered and inline arrangements. The correlations presented in this article are developed based on comprehensive CFD simulations for a large design space and include experimental validation. More than 80% of source data can be predicted within 10% error and more than 90% within 20% error. In this paper we use these correlations to optimize the condenser and evaporator of a 3 ton heat pump unit using R410A as the working fluid. The HX optimization framework uses a Multi-Objective Genetic Algorithm (MOGA) and an in-house HX design tool based on a segmented ε-NTU method. The optimum designs exhibit more than 50% reduction in size, and up to 50% reduction in both air and refrigerant pressure drops, compared to the baseline tube-fin HX’s using tube diameters larger than 7mm. In a system context the optimum HX’s demonstrated the ability to reduce 50% of the refrigerant charge within the HX’s and shifting majority of the system refrigerant mass to the connecting pipes. The COP is improved by 5%-7% for the same capacity

A Model for Performance Prediction of Brazed Plate Condensers with Conventional and Alternative Lower GWP Refrigerants

Plate heat exchangers are used in a wide variety of applications from air-conditioning, refrigeration, food processing, and chemical industry to energy generation systems. Plate heat exchangers are favored because of their compactness, flexible thermal sizing, close approach temperature, pure counter-flow operation, and enhanced heat transfer performance. This paper presents a literature review of available correlations for heat transfer and pressure drop calculations during condensation in brazed plates. Condensation heat transfer in plate heat exchangers can be preliminarily evaluated using the classic Nusselt equation for laminar film condensation on a vertical plate. However, condensation performance is influenced by many factors such as fluid properties, plate geometry, and mass flow rate, and therefore, it is difficult to obtain an ideal correlation which accounts for all these factors. The heat transfer coefficients of different refrigerants, including alternative lower GWP refrigerants R32, D2Y60, and L41a, are computed using heat transfer correlations found in literature. Generally, R32 shows the most favorable heat transfer performance, followed by L41a. An overview on an already existing model that is capable of predicting the performance of plate heat exchangers with generalized multi-fluid and multi-pass configurations is also presented. The model is validated against experimental data for water-to-R134a condenser. A total of sixteen experimental datasets are used. The heat capacity predicted by the model is within ±5% of the measured heat capacity, while most of the predicted outlet temperatures are within ±2 K of measured values

An Improved Moving Boundary Heat Exchanger Model with Pressure Drop

A literature review indicates that almost all moving boundary heat exchanger models used in dynamic simulations of heat pumps rely on the common hypothesis that the refrigerant pressure drop is negligible. In fact, it is important to include the momentum balance in some applications, such as electronics cooling where microchannels are commonly used and significant pressure drop is observed and large-scale heat exchangers in solar thermal plants where tube length can be longer than several hundred meters. In addition, a comprehensive and robust switching approach is needed to handle transitions between different model states due to phase change. It is found that the current switching methods in the literature exhibit several shortcomings which may cause serious errors and stability issues when simulating cycling transients of vapor compression systems. The objective of this paper is to propose an improved moving boundary formulation that aims to fill in the above research gaps. Specifically, two different approaches are presented to account for the refrigerant pressure drop across the heat exchanger. A novel and comprehensive switching scheme is introduced to ensure smooth transition between different model representations under large disturbances. The proposed model is validated using measured data. The validation shows that the proposed heat exchanger model along with other supporting component models can reasonably capture the start-up transients of a flash tank vapor injection heat pump system

Performance Evaluation Criteria & Utility Function for Analysis of Compact Air-to-Refrigerant Heat Exchangers

The Performance Evaluation Criteria (PEC) constitutes a set of metrics that quantifies geometrical characteristics, and performance of a Heat eXchanger (HX) under design and off-design conditions. There is a vast literature describing different PEC methods and it can be separated into two main categories: energy-based and entropy-based metrics. The first include all metrics that directly measure the thermal-hydraulic performance and geometry features such as surface density, face area and aspect ratio. The second approach entails a more fundamental perspective by employing the second law of thermodynamics to determine the best and worst heat transfer surfaces in terms of entropy generation and/or exergy destruction. Usually the second approach brings a broader perspective when evaluating the HX in a system context. From a design viewpoint the choice of PEC is really a matter of preference, as long as the problem specifications are being met. A more challenging task, however, is the selection of the best HX amongst multiple alternatives. More recently, with the great advances in computational tools, a large number of novel HX concepts and multi-objective optimization (MOO) studies are being undertaken. When performing MOO analysis one must be able to understand why did the optimizer selected those optimum designs, and be able to know which one to select from a set of Pareto Optimal designs. In other words, from a decision-making viewpoint the use of PEC’s is less trivial. In this paper we provide a brief review of the available PEC in the literature for HX design. Additionally we present a set of PEC metrics that should be used for selecting a HX amongst multiple optimum designs, sized to perform the same job, i.e. same heat load capacity and fluid states. We developed a utility function, using such metrics that will better assist the decision-maker in selecting the best alternative. This utility function was specifically developed for single-phase air-to-refrigerant HX application, and applied to a case of study consisting of multiple optimum Pareto sets for different surfaces. Additional CFD analysis is also carried out for completeness and to illustrate the underlying physics of the airflow on different surfaces that lead to the differences in performance between different surfaces

Investigation of Thermal-Hydraulic Characteristics of Pillow Plate Heat Exchangers Using CFD

The compactness and desirable thermal characteristics of plate heat exchangers have made them a strong competing heat exchanger technology in the heating, ventilating, air conditioning and refrigeration industry. The miniaturization of plate heat exchangers has become a focal point of attention in recent research. It is desirable to utilize less material and refrigerant charge to obtain the same heat transfer performance. Pillow plate heat exchangers (PPHEs) consist of wavy plates that are welded together with a certain pattern using spot welding, sealed at the edges, and then inflated in a hydroforming process. The complex wavy structure of the pillow plates creates an excellent heat transfer medium with a fully developed turbulent flow between the plates. Thus, PPHEs are used in various single-phase as well as two-phase applications in the industry. This paper presents a parametric study on the effect of critical geometrical parameters and flow conditions, on the thermal-hydraulic performance of PPHEs. The pillow surface is created using a Non-Uniform Rational B-Splines (NURBS) algorithm. The flow between two adjacent pillow plates is then investigated using computational fluid dynamics (CFD). A PPHE with optimum geometric parameters for single-phase water flow is presented