Methodology for the Evaluation of Natural Ventilation in ... - Cham

Chapter 5.0Dimensional Analysis and SimilitudeCertain scaling issues need to be resolved before any conclusions can be drawn from thecomparison of reduced-scale modeling of any kind and the full-scale application. Whenevaluating models at scales smaller than the prototype, the goal is to replicate the behavior offull-scale prototype. This comparison is done by measuring the relevant parameters in thereduced-scale model and by obtaining the values for the prototype using a known scale factor.Both dimensional analysis and similitude must be established for this comparison, as one cannotdefine the other alone. Two systems are said to be similar if their features can be mapped pointby-point,from one region to another region. These regions do not have to be of the same size,and often one is many times smaller. By making the equations that describe the flowdimensionless, the outcome will result in key dimensionless parameters that provide solutionsthat are similar, if the resulting dimensionless parameters are equal. Dimensionless relationshipsare validated through the analysis of equations, while similitude describes the similarity ofbehavior or phenomena. There are some limitations to this approach in meeting all similarityrequirements, as an exact match is virtually impossible at anything other than the same scale asthe prototype, which will be addressed later in this chapter.Experiments are carried out with models for a variety of reasons. Model studies can provide datawhile avoiding costly mistakes and can be used to obtain information that will assist in thedesign of the prototype. Models are relatively inexpensive to build and to modify both in layoutand in construction as compared to full-scale versions. But it is important to first understand thetheory of the phenomenon being studied before attempting to build and evaluate a model for agiven problem statement. It is not useful, and in fact wasteful, to resort to a model study if theresults can be accurately predicted by theory. Often models are used to assess spaces that aredifficult to evaluate, such as spaces in which there is not enough control in the prototype or incases where it is too expensive to outfit the space with the required instrumentation (Szirtes1998). Once the relevant dimensionless products are found from an analysis of the governingequations used in describing the phenomena, then a series of experiments can then be performedto find the functional relationship between the dimensionless parameters. This relationship canthen be used over a much wider range of conditions than those employed for the experiments. Itis crucial that the relevant dimensionless parameters are identified, in addition to the range inwhich they can be used if an exact match is not possible. There are many variables involved andsome means must be used to eliminate those of lesser importance.5.1 Governing EquationsFor both the full scale and the reduced scale physical models and the CFD simulation, there areequations that can be used to describe the flow of the fluid as well as the heat transfer. Theseequations are the conservation of mass, or continuity equation, the conservation of momentum,or Navier-Stokes equation, and the conservation of energy. The models were evaluated forconditions at steady state.83