"Optimization" and HVAC&R.

Optimization is an act, process, or methodology of making something (as a design, system, or decision) as fully perfect, functional, or effective as possible; specifically: the mathematical procedures (as finding the maximum of a function)--Merriam-Webster online dictionary

HVAC&R systems and components optimization can provide a significant reduction in energy consumption and material utilization. This is true only if systematic optimization is performed with the objectives of minimizing the amount of material used and the amount of energy consumed. Furthermore, material utilization and energy consumption minimization would reflect a decrease in life cycle green house gas emissions, which puts us a step closer toward sustainable development.

Currently, the term optimization is being used in HVAC&R to either describe a trial-and-error process of finding the best performance among few alternatives, or the systematic use of optimization techniques to explore the design space in search of a globally optimum design. The first definition, which has long been used in the HVAC&R community, is not an actual optimization. It is actually a simple parametric study that does not assure optimum solutions, because only a small fraction of the solution space is actually explored. The second definition, which is a rigorous definition of optimization, is yet to be comprehensively employed in the industry. The use of optimization, with its rigorous definition, has increased in recent publications; however, the weak definition still exists. The use of optimization with its rigorous meaning ensures that the results are indeed optimum results. The larger the design space gets, the more important systematic optimization becomes. Trial and error techniques, while helpful, will quickly become much less productive as the number of alternative designs increase.

An example of the limitation of the trial and error technique is heat exchanger optimization. Several heat exchanger designs can be used to serve the same load under the same geometrical constraints. However, each design would have different hydraulic performance, volume, and cost. Thus, a simple optimization problem can be formulated to choose the best design. If the design space, for example, includes 2 off-the-shelf tube diameters, a range of acceptable tube lengths--represented by 20 discrete lengths, 5 tube rows, 10 vertical and horizontal tube spacings, 10 fin spacings, 5 fin patterns, and 10 tube circuitries, then the number of possible heat exchanger designs becomes 106 designs. A trial-and-error procedure will not be able to cover the entire design space and would generally provide a design that was not optimum, as designers will try to limit the design space and search between alternatives using their intuition and experience. On the other hand, a systematic optimization technique can search the entire design space, yielding either a local or a global optimum design based on the algorithm being used.

To find the global optimum for the above-mentioned heat exchanger problem, exhaustive search can be used as an alternative method to the trial-and-error procedure. In the exhaustive search, all [10.sup.6] heat exchangers designs need to be evaluated and checked for constraint violations. This method is generally acceptable for a small design space. But even in this simple optimization problem, the exhaustive search becomes computationally expensive. A number of other optimization techniques exist that would systematically search for the global optimum without needing to evaluate the entire design space. The performance of each of these techniques depends greatly on the type of the design space (continuous, discrete, or mixed). The number of optimization objectives (objective functions) is another important factor in the formulation and selection of the optimization technique. In the case of a single objective problem (e.g., minimizing tube and fin materials) there exists either a single or multiple, redundant designs that provide optimum performance. However, in cases of multiple conflicting objectives (e.g. minimizing tube and fin materials and minimizing energy consumption--generally known as multi-objective optimization problem) there exists a set of optimum designs (Pareto set) showing the trade off between competing objectives.

There is a current effort to establish an ASHRAE task group for HVAC&R system and component optimization. This task group will work on increasing ASHRAE membership awareness of optimization techniques and the techniques' impact on HVAC&R systems and components performance improvement. The proposed outcome of this task group is to convince design engineers to use systematic optimization techniques so that, as a step toward sustainable development, they design the best systems and components based on available technologies. Furthermore, the task group will encourage the correct use of the word optimization in the HVAC&R community.

Last but not least, we encourage authors and contributors to HVAC&R Research to be cognizant of this more rigorous definition of the term optimization and to use the word correctly.

Reinhard Radermacher, PhD

Omar Abdelaziz

Fellow Member ASHRAE

Student Member ASHRAE

Reinhard Radermacher is a professor and Omar Abdelaziz is a graduate research assistant in the Department of Mechanical Engineering at the University of Maryland, College Park.