Christopher M. Healey

Potential-Flow Modeling for Data Center Applications

Potential-flow-based airflow and heat transfer models have been proposed as a computationally efficient alternative to the Navier-Stokes Equations for predicting the three-dimensional flow field in data center applications. These models are simple, solve quickly, and capture much of the fluid flow physics, but ignore buoyancy and frictional effects, i.e., rotationality, turbulence, and wall friction. However, a comprehensive comparison of the efficiency and accuracy of these methods versus more sophisticated tools, like CFD, is lacking. The main contribution of this paper is a study of the performance of potential-flow methods compared to CFD in eight layouts inspired by actual data center configurations. We demonstrate that potential-flow methods can be helpful in data center design and management applications.Copyright

Selection Procedures for Simulations with Multiple Constraints under Independent and Correlated Sampling

We consider the problem of selecting the best feasible system with constraints on multiple secondary performance measures. We develop fully sequential indifference-zone procedures to solve this problem that guarantee a nominal probability of correct selection. In addition, we address two issues critical to the efficiency of these procedures: namely, the allocation of error between feasibility determination and selection of the best system, and the use of Common Random Numbers. We provide a recommended error allocation as a function of the number of constraints, supported by an experimental study and an approximate asymptotic analysis. The validity and efficiency of the new procedures with independent and CRN are demonstrated through both analytical and experimental results.

Efficient comparison of constrained systems using dormancy

We consider the problem of finding the best simulated system under a primary performance measure, while also satisfying stochastic constraints on secondary performance measures. We improve upon existing constrained selection procedures by allowing certain systems to become dormant, halting sampling for those systems as the procedure continues. A system goes dormant when it is found inferior to another system whose feasibility has not been determined, and returns to contention only if its superior system is eliminated. If found feasible, the superior system will eliminate the dormant system. By making systems dormant, we avoid collecting unnecessary observations from inferior systems. The paper also proposes other modifications, and studies the impact and benefits of our approaches (compared to similar constrained selection procedures) through experimental results and asymptotic approximations. Additionally, we discuss the difficulties associated with procedures that use sample means of unequal, random sample sizes, which commonly occurs within constrained selection and optimization-via-simulation.

Experimental Measurement of Server Thermal Effectiveness for Compact Transient Data Center Models

Server thermal mass can significantly affect the rate at which a data center heats up following a loss of cooling and moderate transient temperature fluctuations due to changing CPU utilization. Recently, a compact server model has been introduced which captures the effects of thermal mass while avoiding the impractical level of detail that would be required by an explicit representation of all relevant server components. Inputs to that model include server mass, overall effective specific heat, and a parameter called the “server thermal effectiveness”. The latter characterizes the server’s ability to transfer heat to/from the airstream passing through it and can take values between zero (no heat exchange) and one (maximum possible heat exchange). Server thermal mass is a physical property of a server and is not influenced by external factors.In order to use the compact model for practical applications, we must experimentally measure the thermal effectiveness of actual servers. The present study reviews the compact model and describes the development of an experimental technique for measuring thermal effectiveness. The technique is validated using simple plate fin heat sinks in place of an actual server. This “server proxy” is sufficiently simple so that it can be modeled accurately in detail in CFD, providing well-controlled benchmark data. CFD and experimental measurements both yield a value of server thermal effectiveness of approximately 0.6, providing confidence in the model and measurement technique for the future characterization of actual servers.Copyright

A method for predicting key data center temperatures by known airflow streams

We present a simplified model for predicting key data-center temperatures, such as those of rack inlets and cooler returns. If the primary airflow streams into and out of all racks and coolers are known, these airflow values can be combined with the assumption of a well-mixed room ambient volume to create a simplified, but energy-balanced, set of temperature equations. Since the temperature estimates are restricted to only a small number of data center objects, solutions can be found quickly. This temperature model can be adapted to quickly address data center design or management issues without multiple Computational Fluid Dynamics (CFD) simulations. Optimized cooler set points can be quickly found with only slight adjustments to the model. In another application, the effects of cooler capacity models are easily understood when incorporated within the temperature model. The object-averaged inlet temperature estimates generated by this temperature model compare favorably to those found by CFD.

Ranking and selection techniques with overlapping variance estimators

Some ranking and selection (R&S) procedures for steady-state simulation require an estimate of the asymptotic variance parameter of each system to guarantee a certain probability of correct selection. We show that the performance of such R&S procedures depends on the quality of the variance estimates that are used. In this paper, we study the performance of R&S procedures with two new variance estimators --- overlapping area and overlapping Cramer-von Mises estimators --- which show better long-run performance than other estimators previously used in R&S problems.

A minimal switching procedure for constrained ranking and selection under independent or common random numbers

Constrained Ranking and Selection (R&S) aims to select the best system according to a primary performance measure, while also satisfying constraints on secondary performance measures. Several procedures have been proposed for constrained R&S, but these procedures seek to minimize the number of samples required to choose the best constrained system without taking into account the setup costs incurred when switching between systems. We introduce a new procedure that minimizes the number of such switches, while still making a valid selection of the best constrained system. Analytical and experimental results show that the procedure is valid for independent systems and efficient in terms of total cost (incorporating both switching and sampling costs). We also inspect the use of the Common Random Numbers (CRN) approach to improve the efficiency of our new procedure. When implementing CRN, we see a significant decrease in the samples needed to identify the best constrained system, but this is sometimes achieved at the expense of a valid Probability of Correct Selection (PCS) due to the comparison of systems with an unequal number of samples. We propose four variance estimate modifications and show that their use within our new procedure provides good PCS under CRN at the cost of some additional observations.

Compact Modeling of Data Center Air Containment Systems

The practice of ducting racks to a dropped ceiling or containing entire cold or hot aisles in data centers is being implemented with more frequency in an attempt to improve reliability and efficiency. While CFD and other numerical modeling tools are widely used to optimize data center cooling, they are not particularly effective at modeling containment systems; the performance of such systems is dominated by small and complex leakage paths (e.g., through, around, and under racks), which are difficult or impossible to include in a practical full-scale model. We propose a compact model which uses a flow network to determine airflow rates inside containment systems while the traditional “parent” numerical model continues to handle predictions in the rest of the facility. The two models are coupled at flow boundaries such as where ducting meets a dropped ceiling and leakage paths cross rack surfaces. The compact-model approach has the opportunity to be much faster and more robust than fully-explicit CFD models since leakage path resistances can be established through experimental measurements. We discuss the characterization of rack leakage paths and demonstrate the use of the compact model in a full data center simulation in which the role of parent numerical model is played by a potential flow model.Copyright

A minimal switching procedure for constrained ranking and selection

Constrained ranking and selection aims to select the best system according to a primary performance measure, while also satisfying constraints on secondary performance measures. We introduce a new procedure that makes a valid selection of the best constrained system, while minimizing the number of switches between systems. Analytical and experimental results show that the procedure is both valid and efficient in terms of total cost (incorporating both switching and sampling costs).

Creating a Calibrated CFD Model of a Midsize Data Center

Calibrating a CFD model against measured data is the first step to successfully utilizing this technology for change-management and the optimization of an existing data center. To date, there has been very little published on this calibration process; more focus has been placed on the use of CFD at the design stage and the development of modeling techniques and solvers. Further, few studies which feature comprehensive comparisons of CFD-predicted and measured data have been published for real data centers, and many that have, demonstrated only modest agreement at best. This study provides another such comparison — for a 7,400 ft2 (687 m2), 138-rack, raised-floor facility. The goals of the study are to benchmark the level of agreement that can be practically obtained and also to investigate the level of modeling detail required. Additionally, specific practical advice covering both CFD modeling and experimental measurements is provided. A plenum-only CFD model is compared to measured tile airflow rates and a room-model, which uses measured tile flow rates as boundary conditions, is compared to temperatures measured at each rack inlet. The level of agreement is among the best published to date and demonstrates that a CFD model can be adequately calibrated against measured data and is of value for ongoing data center operation.Copyright