A dynamic compact thermal model for data center analysis and control using the zonal method and artificial neural networks
Introduction
Today, the energy consumption of data centers is driving considerable research to achieve better energy efficiency through optimal thermal management in a wide variety of data center configurations for a broad range of operating conditions. Efficient thermal management requires real-time prediction of airflow and temperature distributions and the results must be sufficiently accurate to build a reliable control system. Generally, fully three-dimensional, physics-based flow and temperature modeling using CFD cannot be conducted in real time. The CFD simulations require the use of turbulence models which significantly increase the number of unknowns. In order to incorporate CFD models into control strategies, time-dependent simulations will often be required.
At present, control systems for thermal management are often designed using relatively simple volume averaged compact models (e.g., well-mixed nodal approach). However, it is well-known that the temperature distribution in certain server inlet regions can be sensitively affected by hot air recirculation from the server outlets. The resulting inlet temperatures in the hotspot zones are significantly different from the temperature of the cooling air entering through the perforated floor tiles. This undesirable inlet temperature variation throughout the data center cold aisle space might be significant. This temperature variation is not typically sensed by the air conditioning control systems, and this results in incorrect control actions.
Ideally, an accurate control system requires a compact model to compute the airflow and control the temperature in a more precise way. Proper Orthogonal Decomposition (POD) has been used to optimize data center cooling [1], [2], [3]. POD is capable of providing predictive capability for thermal analysis. However, more generalizable compact models that are capable of extrapolation to a broad range of configurations and operating conditions are needed. Zonal models are regarded as a physically based intermediate approach between CFD and a multi-node lumped model. They are capable of taking various transport phenomena into consideration, such as thermal advection, conduction and radiation in order to calculate energy transport and temperature distributions. The zonal approach applied in Ref. [4] gives reasonably accurate airflow and air temperature results for simple rectangular geometries in 2D and 3D. The model was easily incorporated into a modular simulation and control environment and requires very little computation time. A complex conduction problem was studied in Ref. [5], which demonstrates how the zonal technique can be used for both steady and transient problems. The zonal model in Ref. [6] was formulated to describe the cooling process of distribution transformers. Different generations of zonal models have been developed over the last two decades for applications in building energy usage and ventilation. A momentum zonal model based on the inviscid Euler equations was developed to improve building load and energy simulations by predicting indoor airflows and temperatures [7]. This approach was also employed recently to predict physical parameters in HVAC studies, such as the combination of a system employing both air conditioning and natural ventilation for large enclosures [8], [9]. The study reported in Ref. [10] showed some advantages of zonal modeling over coarse-grid CFD and Fast Fluid Dynamics (FFD). A velocity propagating zonal method was developed and implemented using Modelica to characterize the airflow and temperature patterns in an isothermal room [11]. The broad range of applications indicates that zonal models may be used to predict the flow distribution and spatial temperature variation for the relatively complex room configurations seen in data centers. To the best of our knowledge, this work is the first attempt to utilize the VPM zonal method to develop a compact model for dynamic thermal analysis and control in data centers.
Section snippets
Data center computational model
In order to develop the zonal model, first a model for a basic raised floor data center configuration was built and analyzed using the commercial, finite-volume CFD software package FloTHERM. Different views of the data center model configuration are shown in Fig. 1. The room has a single computer room air conditioning (CRAC) unit located on the right end. The cooling air from the CRAC is delivered through the plenum (outlined in purple) into the cold aisle. The present study focuses on the use
Zonal method
Zonal models are able to predict pressure, temperature and mass flow rates based on integrated forms of conservation laws and different modes of thermal transport [13], [14]. The fundamental conservation laws are applied to each zonal volume. The usual form of the conservation laws are written as follows:where is the interfacial mass flow rate, ϕ is the energy, P is pressure, ρ is the
The case study
To apply the VPM based zonal model, the contained cold aisle data center configuration was divided into zones or cells. Shown in Fig. 2(c), one half of the symmetric data center configuration is divided into 45 cubic zonal volumes or cells (5 partitions in the x direction and 3 partitions in each of the y and z directions). In order to formulate the model equations, there are 45 cell objects and 144 interface objects (66 zone-to-zone interfaces and 78 zone-to-surface interfaces). The cell and
The zonal model based state space model
In accordance with the formulation used in the CFD model [16], [17], [18], the energy equation can be expressed as:Eq. (8) is discretized using the finite volume approach (compass notation) as follows:
Eq. (10) shows the coefficient in the finite volume difference equation formulated on the bottom side (the same rule applies in the other directions, see Refs. [16], [18] for more details).where
Results and discussion
Fig. 8(b) and (c) shows the speed (m/s) calculated at the region outlined in yellow in Fig. 8(a) for the CFD and the zonal model results, respectively. To make an appropriate comparison between the CFD and the zonal model results, the flow and temperature field values from the CFD simulations are volume-averaged over the partitioned zones (e.g. cell 1–cell 4 outlined in red in Fig. 3). These contours are created by interpolating between the temperature values for each of the cells. The zonal
Conclusions
An improved compact model, based on the zonal approach, for analyzing the flow and temperature of a single, contained cold aisle data center has been developed. Also, by coupling the zonal model and an artificial neural network, a control scheme involving a PID controller was given to improve the thermal control in data centers. The zonal model was partially constructed and verified using CFD simulation results. A contained cold-aisle model was used to test the performance of the VPM zonal
Acknowledgements
This research was funded by the Small Scale Systems Integration and Packaging Center (S3IP) at Binghamton University. S3IP is a New York State Center of Excellence and receives funding from the New York State Office of Science, Technology and Innovation (NYSTAR), the Empire State Development Corporation, and a consortium of industrial members.
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