Thesis (M.S.)--Ohio University, August, 1996. / Title from PDF t.p.

Data centers are computing infrastructure facilities used by industries with large data processing needs and the rapid increase in power density of high performance computing equipment has caused many thermal issues in these facilities. Systems-level thermal management requires modeling and analysis of complex fluid flow and heat transfer processes across several decades of length scales. Conventional computational fluid dynamics and heat transfer techniques for such systems are severely limited as a design tool because their large model sizes render parameter sensitivity studies and optimization impractically slow. The traditional proper orthogonal decomposition (POD) methodology has been reformulated to construct physics-based models of turbulent flows and forced convection. Orthogonal complement POD subspaces were developed to parametrize inhomogeneous boundary conditions and greatly extend the use of the existing POD methodology beyond prototypical flows with fixed parameters. A flux matching procedure was devised to overcome the limitations of Galerkin projection methods for the Reynolds-averaged Navier-Stokes equations and greatly improve the computational efficiency of the approximate solutions. An implicit coupling procedure was developed to link the temperature and velocity fields and further extend the low-dimensional modeling methodology to conjugate forced convection heat transfer. The overall reduced-order modeling framework was able to reduce numerical models containing 105 degrees of freedom (DOF) down to less than 20 DOF, while still retaining greater that 90% accuracy over the domain. Rigorous a posteriori error bounds were formulated by using the POD subspace to partition the error contributions and dual residual methods were used to show that the flux matching procedure is a computationally superior approach for low-dimensional modeling of steady turbulent convection. To efficiently model large-scale systems, individual reduced-order models were coupled using flow network modeling as the component interconnection procedure. The development of handshaking procedures between low-dimensional component models lays the foundation to quickly analyze and optimize the modular systems encountered in electronics thermal management. This modularized approach can also serve as skeletal structure to allow the efficient integration of highly-specialized models across disciplines and significantly advance simulation-based design.

The complex turbulent flow regimes encountered in many thermal-fluid engineering applications have proven resistant to the effective application of systematic design because of the computational expense of model evaluation and the inherent variability of turbulent systems. In this thesis the integration of the Proper Orthogonal Decomposition (POD) for reduced order modeling of turbulent convection with the application of robust design principles is proposed as a practical design approach. The POD has been used successfully to create low dimensional steady state flow models within a prescribed range of parameters. The underlying foundation of robust design is to determine superior solutions to design problems by minimizing the effects of variation on system performance, without eliminating their causes. The integration of these constructs utilizing the compromise Decision Support Problem (DSP) results in an efficient, effective robust design approach for complex turbulent convective systems. The efficacy of the approach is illustrated through application to the configuration of data center server cabinets. Data centers are computing infrastructures that house large quantities of data processing equipment. The data processing equipment is stored in 2 m high enclosures known as cabinets. The demand for increased computational performance has led to very high power density cabinet design, with a single cabinet dissipating up to 20 kW. The computer servers are cooled by turbulent convection and have unsteady heat generation and cooling air flows, yielding substantial inherent variability, yet require some of the most stringent operational requirements of any engineering system. Through variation of the power load distribution and flow parameters, such as the rate of cooling air supplied, thermally efficient configurations that are insensitive to variations in operating conditions are determined. This robust design approach is applied to three common data center server cabinet designs, in increasing levels of modeling detail and complexity. Results of the application of this approach to the example problems studied show that the resulting thermally efficient configurations are capable of dissipating up to a 50% greater heat load and 15% decrease in the temperature variability using the same cooling infrastructure. These results are validated rigorously, including comparison of detailed CFD simulations with experimentally gathered temperature data of a mock server cabinet. Finally, with the approach validated, augmentations to the approach are considered for multi-scale design, extending approaches domain of applicability.