Exploration of a Potential-Flow-Based Compact Model of Air-Flow Transport in Data Centers

This paper summarizes an exploration of a compact model of air flow and transport in data centers developed from potential flow theory. Boundaries for the airflow in the data center are often complex due to the numerous rows of servers and other equipment in the facility, and there are generally multiple air inlets and outlets, which produce a fairly complex three-dimensional flow field in the air space in the data center. The general problem of airflow and convective transport in a data center requires accurate treatment of a turbulent flow in a complex flow passage with some buoyancy effects. As a result, full CFD thermofluidic models tend to be time-consuming and tedious to set up for such complex flow circumstances. In this initial study, we formulated an approximate model that retains only the most basic physical mechanisms of the flow. The resulting model of air flow in the data center is based on potential flow theory, which is exact for irrotational inviscid flow. The temperature field resulting from server heat input is determined by solving the convective energy transport equation along potential flow streamlines. This innovative approach, which takes advantage of the irrotational character of the modeled flow, provides a fast computational method for determining the temperature field and convective transport of thermal energy in the data center. Computations to predict the three-dimensional flow and temperature fields with the model typically require less than 60 seconds to complete on a laptop computer. Flow and temperature field results predicted by the model for typical data center flow circumstances are presented and limitations of the model are assessed. Features of an intuitive graphical user interface for the model that simplifies input of the data center design parameters are also described. Results for case studies indicate low sensitivity to mesh size and convergence criteria. Although the flow and temperature field models developed here are more approximate than full CFD methods, they are good first approximations that provide the means to rapidly explore the parameter space for the data center design. This model can be used to quickly identify the optimal region of the design space, whereupon a more detailed CFD modeling can be used to fine-tune an optimal design. The results of this investigation demonstrate that this type of fast compact model can be a very useful tool when used as a precursor to full CFD modeling in data center design optimization.