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%

Comparison Of Approximation-assisted Component Modeling Methods For Steady State Vapor Compression System Simulation

An accurate, fast and robust heat exchanger model is critical for reliable steady state simulation of vapor compression systems. In such simulations, the heat exchanger models are often the most time consuming components and can be plagued by severe non-linearities especially if they are black-box or third-party provided. This paper investigates and compares different approaches for heat exchanger performance approximation, with the distributed parameter approach being the baseline. The methods are: Gaussian kernel based on Kriging, a multi-zone approach, and polynomial regression. Generally, distributed parameter models have the highest level of accuracy but can be time-consuming. Kriging metamodels have relatively low computational cost but has little underlying physics. Multi-zone models have the lowest computation cost due to the lump treatment of heat transfer and pressure drop; however, they also tend to have the least accuracy. To better understand the potential and limitations of those heat exchanger modeling methods, the pressure drop and capacity of the same heat exchangers predicted by the three approximation modeling methods are compared against the baseline approach under the same operating conditions. The comparison between the Kriging metamodel and the distributed parameter model shows that 95.2% out of 10,000 test points have capacity deviation less than 20%, and that 93.9% have pressure drop deviation less than 10%. Large capacity deviations occur at those operating conditions with low inlet pressures, while large pressure drop deviations occur at those with high inlet pressures. The multi-zone model presents relatively larger deviations in terms of both pressure drop and capacity when compared with the distributed parameter model. Thus, regression based techniques are applied to further improve the accuracy of the multi-zone model. The heat exchanger modeling approaches are incorporated to a vapor compression cycle model. Lastly, some ideas on how such an approach can be used to approximate a set of components models, not just heat exchangers, are discussed

Review of Shape and Topology Optimization for Design of Air-to-Refrigerant Heat Exchangers

Air-to-refrigerant heat exchangers (HXs) have been the topic of exhaustive research as they are fundamental components of HVAC&R systems. It has been well-established that the large airside thermal resistance dominates the HX thermal resistance, and thus significant research efforts have focused on improving the air-side performance of these heat exchangers. As HXs continue to become more compact, thermal resistance reduction is typically realized through the utilization of extended secondary heat transfer surfaces such as fins. However, past research has shown that the thermal-hydraulic trade-offs provided by fins are often not attractive enough to warrant their use, especially for small diameter tubes. Yet, the inadequate primary surface area provided by compact HXs essentially mandate the necessity of fins to meet thermal resistance requirements. In recent years, advancements in computational tools such as Computational Fluid Dynamics (CFD) and optimization algorithms, coupled with the advent of additive manufacturing technologies, have allowed engineers to expand conventional HX design ideologies to include such concepts as shape and topology optimization. This lends itself directly to primary heat transfer surface optimization and even the potential removal of finned surfaces altogether. This paper presents a comprehensive literature review investigating air-to-refrigerant HX shape and topology optimization. The fundamentals of both shape and topology optimization, model development, and experimental validations are all separately discussed. Studies featuring manufactured prototypes and/or experimentally validated optimal designs are treated with additional emphasis. This paper concludes by identifying key research gaps and proposing future research directions for HX shape and topology optimization

Tube-Fin Heat Exchanger Circuitry Optimization Using Integer Permutation Based Genetic Algorithm

Tube-fin heat exchangers (HXs) are widely used in air-conditioning and heat pumping applications. The performance of these heat exchangers is strongly influenced by the refrigerant circuitry, i.e. the refrigerant flow path along the different tubes in the HX core. Since for a given number of tubes, the number of possible circuitries is exponentially large, neither the exhaustive search nor traditional optimization algorithms can be used to optimize the circuitry for a given application. Researchers have previously used Genetic algorithms (GA) coupled with a learning module to solve this problem, but there is no guarantee that the resulting circuitry can be manufactured in a cost-effective manner. In this paper, we present a GA-based integer permutation approach for solving the circuitry optimization problem. A finite volume heat exchanger simulation tool is used to simulate the performance of different circuitries generated by the optimizer. The crossover, mutation and individual generation genetic operators are designed such that all individuals generated by the GA are in the feasible domain. The proposed approach can explore the solution space more efficiently than a conventional GA. Exhaustive search and results from the literature are used to verify the results obtained from the proposed optimization scheme for small heat exchangers. The result shows that integer permutation based GA (IPGA) is capable of finding optimal or near-optimal refrigerant circuitry designs using a relatively low population size and iterations. Furthermore, the limits on in-tube refrigerant mass flux obtained from empirical data, are used to assist the IPGA. The manufacturability aspect is handled using a constraint-dominated sorting in the fitness assignment stage of GA with a goal of obtaining the shortest tube joints. It is shown that the proposed constraint handling technique significantly improves the manufacturability of the optimal circuits. Overall, the analyses of several test heat exchanger cases show that the constrained integer permutation based GA can generate circuitry designs with capacities superior to those obtained manually and are manufacturable. Compared to a conventional GA, it exhibits faster convergence and higher quality optimal solutions. In addition, a 3.1-8.8% increase in heat exchange capacity is obtained by IPGA compared with the conventional counter-flow circuitry

Tube-Fin Heat Exchanger Circuitry Optimization for Multiple Airflow Maldistribution Profiles

Tube-fin heat exchangers(HXs) are widely used in the HVAC&R industry. Studies have proved that by optimizing the refrigerant circuitry, heat exchanger performance can be significantly improved. Since air-to-refrigerant heat exchangers are typically confined in packaged units along with a fan, the airflow distribution on the face of the HXs is a dominant factor influencing its performance. During the operation of a heat exchanger as a part of the system, the air flow distribution changes continuously, especially as the fan speed changes during startup and shutdown cycles. This poses a design challenge as typically heat exchangers are designed using the assumption of uniform flow or for a single known flow distribution profile. For each profile and for the same flow rate, a typical circuitry optimization algorithm can generate a completely different optimal circuitry. Therefore, robust circuitry design that can always guarantee an acceptable minimum performance under various airflow distributions is required. In the field of optimization, this is referred to as robust optimization. This paper presents a robust circuitry design optimization approach. The formulation consists of an upper-level optimization problem and a lower-level finite search problem. In the lower-level problem, a finite number of typical airflow distribution profiles are imposed. These profiles are obtained from the literature, experimental measurements, and CFD simulations. The goal of the lower-level finite search problem is to obtain the worst case capacity degradation from different air flow profiles for a given circuitry. The objective of the upper-level problem is to obtain the circuitry that maximizes the worst case capacity subject to a set of operating constraints such as pressure drops and subcooling/superheat. In order to effectively obtain the optimal designs and guarantee manufacturable designs, an integer permutation based genetic algorithm (IPGA) developed in previous research is used to solve the upper-level problem. The optimized circuitry is then verified by using exhaustive search. The comparison between the solutions of the proposed approach and the optimal circuitries obtained under uniform airflow distribution shows that despite a 1.4%-3.7% decrease in capacity, robust circuitry designs are more resilient to multiple airflow maldistribution profiles. The proposed approach is applied to an A-type indoor unit which demonstrates its applicability in real-world design

Weld Shape Optimization for Pillow Plate Heat Exchangers

Miniaturization of Plate Heat Exchangers (PHXs) is becoming a central research topic in order to utilize less material and less refrigerant charge to attain similar heat transfer performance, and hence contribute significantly into energy conservation and lower environmental impact. Thus, it is greatly desirable to obtain new designs to achieve this goal. Pillow Plate Heat Exchanger (PPHX) is a type of PHXs with a 3D complex wavy structure, but yet an economical manufacturing process positioning itself as a potential strong competitor among other types of PHXs. PPHXs have the advantage of simple manufacturing process which gives it great design flexibility, and allows new designs to be created simpler and less costly. However, PPHXs are more commonly found in chemical and process industry. Research on PPHXs in HVAC&R is very limited. It is desired to make use of PPHXs advantages in HVAC&R applications. This can be done by creating more efficient designs. The thermal-hydraulic performance of PPHXs is primarily altered by the weld shape, size, and pattern, as well as the pillow height. The shape, and size of the weld is one of the most sensitive parameters affecting the thermal-hydraulic performance of PPHXs. As the weld size is smaller and more streamlined, the pressure drop is reduced significantly. However, the heat transfer area is also reduced using a more streamlined weld shape. In this study, new designs for PPHXs are investigated using different weld shapes that are represented using Non-Uniform Rational B-Splines (NURBS. Each control point in the NURBS curve is a design parameter in the optimization problem. The optimization problem has 11 design parameters. The whole CFD simulation is automated using Parallel Parameterized CFD (PPCFD). Since the CFD simulation of 3D PPHXs is computationally very expensive, the automated CFD simulations and Approximation Assisted Optimization (AAO) reduce the computational time and resources required significantly. A meta-model, using Kriging method, is calculated and verified using random samples from the design space. Multi-Objective Genetic Algorithm (MOGA) utilizes the verified meta-model to calculate optimum designs which have the optimum weld shape and size. The potential enhancement can be up to 50% improvement in heat transfer coefficient and 20% reduction in pressure drop as compared to a selected PPHX baseline design. The optimum designs are also compared to optimum designs of PPHXs with circular spot welds. The potential improvement can be up to 20% in both heat transfer coefficient, and pressure drop

Heat Transfer Enhancement Using Approximation Assisted Optimization for Pillow Plate Heat Exchangers

Optimization is a powerful mathematical methodology that can be employed to miniaturize and improve the performance of plate heat exchangers in order to achieve higher levels of energy efficiency. Achieving these goals means less material used, and less charge, and thus a lower impact on the environment Plate heat exchangers (PHXs) are favored by the HVAC&R industry since they combine between the advantages of compactness, and desirable thermal-hydraulic characteristics due to their small approach temperature. However, the challenge with plate heat exchangers lies within the costly new designs. Pillow plate heat exchanger (PPHX) is a promising type of PHXs which also possesses desirable thermal-hydraulic characteristics due to their complex 3D wavy structure which creates a fully developed turbulent flow enhancing heat transfer. Furthermore, PPHXs are manufactured in a simpler more economical way compared to conventional PHXs. In this study, hundreds of new designs for PPHXs are investigated in order to maximize the thermal-hydraulic performance. The geometrical characteristics for the PPHXs are varied including pillow height, spot welds pitch ratio, and spot diameter. The PPHX pillow surface is created using CFD simulations ensuring structural stability while resembling the manufacturing process. The computational domain is then obtained from the deformed surface, meshed, and simulated. The whole CFD simulation process with its different components is automated using a Python script. The Latin Hypercube Sampling (LHS) is used to sample points from the design space, and the meta-modeling is calculated using the Kriging method. The optimization problem has four design variables which are the spot weld ratio, the spot weld diameter, the pillow height, and the inlet velocity. The objective is to maximize the heat transfer coefficient and minimize the pressure drop per unit length. The potential enhancement is found to be up to 3 times improvement in heat transfer coefficient and up to 98% reduction in pressure drop as compared to a selected PPHX baseline design. Sensitivity analysis is conducted on the optimal designs to provide insights into factors affecting their performance. The sensitivity study shows that the spot weld diameter is a significant parameter where further improvements can be applied. A comparison of optimal PPHX designs with Chevron PHXs shows that the optimal designs possess a higher heat transfer coefficient at similar values of pressure drop, as high as 3 times at low pressure drop values, and about 23% higher at moderate pressure drop values. It also show that optimum PPHXs designs have lower pressure drop at similar values of heat transfer coefficient, as low as 30%

Impact of Liquid/Vapor Maldistribution on the Performance of a Plate Heat Exchanger Evaporator for Pure and Mixed Refrigerants

This paper presents an estimation of the degradation in heat transfer performance in plate heat exchanger (PHE) evaporators due to flow maldistribution. A booster heat pump system integrated in a district heating network is used as a case study. Butane and two zeotropic mixtures, namely Propylene/Butane (0.5/0.5) and R1234yf/R1233zdE (0.5/0.5) were evaluated as working fluids. The PHE was preliminarily sized for all the refrigerants by considering a fixed plate geometry from a commercial manufacturer. A two-dimensional (2D) numerical model was developed for the evaluation of the total heat flow rate degradation due to the imposed uneven liquid/vapor distribution at the inlet of the PHE channels. Butane showed the most sensitivity to both the effect of end plates and maldistribution, with an overall reduction of the heat flow rate equal to -11.2 %. Both the zeotropic mixtures were insignificantly affected by the uneven quality distribution at the inlet, and suffered a slight reduction of the overall heat flow rate of -0.861 % and -0.779 %, due to effect of end plates. Last, the sensitivity to the boundary conditions of the case study was assessed for the mixture Propylene/Butane (0.5/0.5), evaluating the dependence of the obtained results from superheat and number of channels, since both parameters impact the degradation of heat transfer performanc

A Review of Recent Advances in Additively Manufactured Heat Exchangers

Heat exchangers are a recurrent element found in an abundant number of mechanical engineering systems. The design of these heat exchangers has generally remained static due to manufacturing limitations. However, recently additive manufacturing has facilitated the production of new and previously impossible heat exchanger geometries and structures by fabricating one monolithic build layer-by-layer. For example, Direct Metal Laser Sintering (DMLS) creates approximately 20-micron thick metal layers stacked on top of one another to create a cohesive metal part. Heat exchangers can be constructed in the same way. Improvements of an additively manufactured heat exchanger include using less material, reduced volume, increased thermal performance, increased reliability, and the potential to use new materials. This paper reviews the most recent developments of additively manufactured heat exchangers. Additive manufacturing is not limited to just traditional metal heat exchangers. Indeed, heat exchangers can be constructed from both ceramic and polymer materials as well. The major geometric properties that affect heat exchangers’ thermal performance are discussed. With these advancements, the question posed is whether these additive manufacturing processes can be cost competitive with traditional manufacturing techniques or if there exists a hybrid approach that takes advantages of both technologies. Lastly, the needs for further research and development of additive manufacturing of heat exchangers are discussed

Comparison of Two Object-Oriented Modeling Environments for the Dynamic Simulations of a Residential Heat Pump

Object-oriented physical-modelling platforms greatly facilitate the task of the modelling engineer by abstracting away a lot of the complexity associated with sorting the governing equations and also the nuances of the numerical methods used for solving the differential-algebraic equations (DAEs). For this reason, they have been steadily gaining in popularity in the field of thermofluid simulations. In this study, we compare two platforms of this type: Dymola and EcosimPro. Dymola is a physical modelling environment originally developed at Lund University and now being developed by Dassault Systèmes, and is a commercially available implementation of the open-source physical modelling language Modelica. EcosimPro is a proprietary tool developed by Empresarios Agrupados A.I.E originally for the European Space Agency and now sold to the general public. Both platforms utilise object-oriented modelling paradigms such as multiple inheritance, encapsulation (of behaviour within classes), abstraction (hiding model complexity from the user) and acausal equation handling (equations may be written in any order). We use these platforms to conduct a realistic exercise of modelling and simulating a relatively complex residential heat pump system in both heating and cooling modes and comparing the results against measured data. Component libraries have been prepared in both the platforms for modelling system components. Two-phase flow has been accounted for using slip-ratio based void fraction correlations. In general, the component models have been kept as similar as possible between the two platforms. The heat pump under investigation is a residential, 3-ton unit with a scroll compressor. The cooling mode uses a thermostatic expansion valve (TXV) as the expansion device while the heating mode uses a short-tube orifice. A reversing valve controls the flow direction. The heat pump has been tested under both heating and cooling modes as per ASHRAE’s Standard 116-2010 cyclic test conditions. The measured values have been compared against simulations results from both platforms. The refrigerant pressures and temperatures and the heat exchanger air outlet temperatures are compared. The indoor unit air-side capacity and the compressor power consumption integrated over the on-period are also compared. Additionally, the Seasonal Energy Efficiency Ratio (SEER), the Cooling Load Factor (CLF) and the Cyclic Degradation Coefficient (Cd) are compared which help quantify the performance of the heat pump. Finally, qualitative comparisons of the transients associated with the refrigerant charge migration after shutdown have been made, as this migration is responsible for cycling losses associated with dynamic heat pump operation. The two platforms prove to be similarly capable at simulating an advanced cycle. Both platforms can predict the pressure and temperature transients during the on-off cycling of the heat pump, as well as the performance parameters such as accumulated capacities and the SEER rating. Finally, both ­models predict the simulated charge to be within 80% of the actual charge, which enables a more realistic depiction of system transients