Transient modeling and validation of chilled water based cross flow heat exchangers for local on-demand cooling in data centers

Hybrid air/liquid cooling systems used in data centers enable localized, on-demand cooling, or “smart cooling” using various approaches such as rear door heat exchangers, overhead cooling systems and in row cooling systems. These systems offer the potential to achieve higher energy efficiency by providing local cooling only when it is needed, thereby reducing the overprovisioning that is endemic to traditional systems. At the heart of all hybrid cooling systems is an air to liquid cross flow heat exchanger which regulates the amount of cooling that the system provides by modulating the liquid or air flows or temperatures. Understanding the transient response of the heat exchanger is crucial for the precise control of the system. In this paper a 12 in. × 12 in water to air heat exchanger, with similar characteristics to the heat exchanger commonly found in data centers, is modeled using three partial differential equations solved by the use of a finite difference approach. The model is validated against experimental data obtained from an experimental rig designed to introduce controlled transient perturbations in temperature and flow on the inlet air and liquid flows to the heat exchanger. Experimental data were obtained for step change, ramp change, and sinusoidal variation in the inlet water temperature and mass flow rate. Steady state heat transfer coefficients are used in the air and liquid side of the heat exchanger. The heat transfer coefficient inside the tubes is calculated by the use of the Gnielinski correlation. A steady state technique is used to extract the air side heat transfer coefficient. With these parameters, it was found that the dynamic heat exchanger model agrees remarkably well with the transient experimental data. The modeling equations also provide insight into the characteristic response times of the heat exchanger in terms of the major independent non-dimensional parameters describing its design and operating conditions.