Reduced Order Modeling of Steady Turbulent Convection Flows Using the POD Available to Purchase

In the characterization and design of complex distributed parameter thermo/fluid systems, detailed experimental measurements or fine numerical calculations often produce excessively large data sets, rendering more advance analyses inefficient or impossible. Acquiring the experimental or numerical data is usually a time consuming task, severely restricting the number and range of parameters and ultimately limiting the portion of the design space that can be explored. To develop low dimensional models, it is desirable to decompose the system response into a series of dominant physical modes that describe the system, while incurring a minimal loss of accuracy. The proper orthogonal decomposition (POD) has been successful in creating low dimensional dynamic models of turbulent flows and here its utility is extended to produce approximate solutions of steady, multi-parameter RANS simulations within predefined limits. The methodology is illustrated through the 2-dimensional analysis of an air-cooled data processing cabinet containing 10 individual servers, each with their own flow rate. The results indicate that a flux matching procedure can reduce the model size by 4 orders of magnitude while adequately describing the airflow transport properties within engineering accuracy. This low dimensional description of the flow inside the data processing cabinet can in turn be used to further explore the design space and efficiently optimize the system.